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                <?php  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                namespace Samsara\Fermat\Provider;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                use Samsara\Exceptions\UsageError\IntegrityConstraint;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    6
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                use Samsara\Fermat\Numbers;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    7
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                use Samsara\Fermat\Types\Base\DecimalInterface;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    8
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                use Samsara\Fermat\Types\Base\NumberInterface;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                class SequenceProvider  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    12
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                    13
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                    const EULER_ZIGZAG = [  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    14
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                        '1',                                                // 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    15
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                        '1',                                                // 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    16
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                        '1',                                                // 2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    17
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                        '2',                                                // 3  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    18
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                        '5',                                                // 4  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    19
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                        '16',                                               // 5  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    20
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                        '61',                                               // 6  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    21
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                        '272',                                              // 7  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    22
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                        '1385',                                             // 8  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    23
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                        '7936',                                             // 9  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    24
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                        '50521',                                            // 10  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    25
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                        '353792',                                           // 11  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    26
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                        '2702765',                                          // 12  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    27
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                        '22368256',                                         // 13  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    28
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                        '199360981',                                        // 14  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    29
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                        '1903757312',                                       // 15  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    30
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                        '19391512145',                                      // 16  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    31
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                        '209865342976',                                     // 17  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    32
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                        '2404879675441',                                    // 18  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    33
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                        '29088885112832',                                   // 19  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    34
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                        '370371188237525',                                  // 20  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    35
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                        '4951498053124096',                                 // 21  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    36
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                        '69348874393137901',                                // 22  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    37
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                        '1015423886506852352',                              // 23  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    38
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                        '15514534163557086905',                             // 24  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    39
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                        '246921480190207983616',                            // 25  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    40
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                        '4087072509293123892361',                           // 26  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    41
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                        '70251601603943959887872',                          // 27  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    42
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                        '1252259641403629865468285',                        // 28  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    43
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                        '23119184187809597841473536',                       // 29  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    44
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                        '441543893249023104553682821',                      // 30  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    45
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                        '8713962757125169296170811392',                     // 31  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    46
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                        '177519391579539289436664789665',                   // 32  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    47
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                        '3729407703720529571097509625856',                  // 33  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    48
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                        '80723299235887898062168247453281',                 // 34  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    49
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                        '1798651693450888780071750349094912',               // 35  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    50
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                        '41222060339517702122347079671259045',              // 36  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    51
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                        '970982810785059112379399707952152576',             // 37  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    52
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                        '23489580527043108252017828576198947741',           // 38  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    53
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                        '583203324917310043943191641625494290432',          // 39  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    54
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                        '14851150718114980017877156781405826684425',        // 40  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    55
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                        '387635983772083031828014624002175135645696',       // 41  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    56
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                        '10364622733519612119397957304745185976310201',     // 42  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    57
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                        '283727921907431909304183316295787837183229952',    // 43  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    58
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                        '7947579422597592703608040510088070619519273805',   // 44  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    59
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                        '227681379129930886488600284336316164603920777216', // 45  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    60
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                        '6667537516685544977435028474773748197524107684661',// 46  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    61
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                        '199500252157859031027160499643195658166340757225472',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    62
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                        '6096278645568542158691685742876843153976539044435185',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    63
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                        '190169564657928428175235445073924928592047775873499136',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    64
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                        '6053285248188621896314383785111649088103498225146815121',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    65
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                    ];  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    66
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * OEIS: A005408  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param $n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    71
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    72
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                     * @return DecimalInterface|NumberInterface  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    73
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    74
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                    public static function nthOddNumber($n)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    75
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                    { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    76
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                    77
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                        $n = Numbers::makeOrDont(Numbers::IMMUTABLE, $n, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    78
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                    79
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                        return $n->multiply(2)->add(1);  | 
            
                            
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                    80
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                    81
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    84
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                     * OEIS: A005843  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    85
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    86
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                     * @param $n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    87
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    88
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                     * @return DecimalInterface|NumberInterface  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
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                    89
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                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    90
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                    public static function nthEvenNumber($n)  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    91
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                    { | 
            
            
                                                                        
                            
            
                                    
            
            
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                    92
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                    93
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                        $n = Numbers::makeOrDont(Numbers::IMMUTABLE, $n, 100);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    94
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                    95
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                        return $n->multiply(2);  | 
            
                            
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                    96
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                    97
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    98
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                    99
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    100
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                     * @param $n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    101
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    102
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                     * @return DecimalInterface|NumberInterface  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    103
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    104
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                    public static function nthPowerNegativeOne($n)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    105
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                    { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    106
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                    107
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                        $negOne = Numbers::makeOrDont(Numbers::IMMUTABLE, -1, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    108
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                    109
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                        return $negOne->pow($n);  | 
            
                            
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                    110
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                    111
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    112
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                    113
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    114
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                     * @param $n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    115
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                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    116
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                     * @return DecimalInterface|NumberInterface  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    117
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                     * @throws IntegrityConstraint  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    118
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    119
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                    public static function nthEulerZigzag($n)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    120
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                    { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    121
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                    122
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                        $n = Numbers::makeOrDont(Numbers::IMMUTABLE, $n, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    123
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                    124
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                        if ($n->isGreaterThan(45)) { | 
            
                            
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                    125
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                            throw new IntegrityConstraint(  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    126
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                                '$n cannot be larger than 39',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    127
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                                'Limit your use of the Euler Zigzag Sequence to the 39th index',  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    128
                 | 
                                    
                                                     | 
                
                 | 
                                'This library does not support the Euler Zigzag Sequence (OEIS: A000111) beyond E(39)'  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    129
                 | 
                                    
                                                     | 
                
                 | 
                            );  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                        }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                        return Numbers::make(Numbers::IMMUTABLE, static::EULER_ZIGZAG[$n->asInt()], 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                    public static function nthSecTanCoefSequence($n)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                    { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                        $n = Numbers::makeOrDont(Numbers::IMMUTABLE, $n, 100);  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                        $pi = Numbers::makePi();  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                        $two = Numbers::make(Numbers::IMMUTABLE, 2, 100);  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
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                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                     * WARNING: This function is VERY unoptimized. Be careful of large m values.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                     * @param $n  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                     * @return DecimalInterface|NumberInterface  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                    public static function nthBernoulliNumber($n)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                    { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                        $n = Numbers::makeOrDont(Numbers::IMMUTABLE, $n, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                        if ($n->isEqual(0)) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                            return Numbers::makeOne();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                        } elseif ($n->isEqual(1)) { | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                            return Numbers::make(Numbers::IMMUTABLE, '0.5', 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                        }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                        if ($n->isGreaterThan(1) && $n->modulo(2)->isEqual(1)) { | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                            return Numbers::makeZero();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                        }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                        $b = Numbers::make(Numbers::IMMUTABLE, -1, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                        $two = Numbers::make(Numbers::IMMUTABLE, 2, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                        $four = Numbers::make(Numbers::IMMUTABLE, 4, 100);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                        $b = $b->pow($n->divide(2)->floor())  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                            ->multiply($n->divide($two->pow($n)->subtract($four->pow($n))))  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                            ->multiply(static::nthEulerZigzag($n));  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                        return $b;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                }  | 
            
            
                        
It seems like the method you are trying to call exists only in some of the possible types.
Let’s take a look at an example:
Available Fixes
Add an additional type-check:
Only allow a single type to be passed if the variable comes from a parameter: