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- #!/usr/bin/ruby
- # Primes p such that 8 consecutive primes starting with p are {1,2,3,4,5,6,7,8} modulo 13.
- # https://oeis.org/A338394
- var arr = [
- 5129602609, 40602028559, 69528307577, 129007460609, 236659873633, 322320688171, 371170549153, 390581208473, 441568239503, 651686524243, 761457812389, 807722926973, 855088513163, 855969933859, 977398008289, 1034360135849, 1079253721703, 1348188886799, 1606702635149, 1824535827869, 2084867892589, 2112142435703, 2838797014093, 3025107969053, 3556206499249, 4117239042619, 4130461496851, 4357514052503, 4836054169103, 4908946925273, 18866578471547, 22427393658073, 22835274705283, 31675129703309, 39839235929663, 40583190994529, 42923079229213, 45749347176209, 52780474235243, 58217172986129, 60628028874089, 60981093008239, 68426419393099, 71197879421423, 71481160182979, 81240600887759, 93595283908439,
- 1824535827869, 14161747729169, 14247819770939, 27305880660449, 35265377552159, 36951194202599, 42372979438739, 43554899867519, 43628325363299, 43896197331299, 49965317538449, 53195202089069, 55484434190849, 58548625620239, 60628028874089, 61230871946999, 61508898520109, 61782463362569, 62260651274849, 65552962831019, 67405791008219, 67754204383529, 77202688959059, 78198493331999, 78866151125789, 81240600887759, 93595283908439, 99680785749299
- ].sort.uniq
- assert(arr.all{.is_prime})
- for p in (arr) {
- assert_eq(8.n_primes(p).map{_ % 13}, @(1..8))
- }
- arr.each{|p|
- 12.n_primes(p).map{_ % 13}.say
- }
- say arr.grep { 9.n_primes(_).map{_ % 13} == @(1..9) }
- # Terms congruent to {1..9} mod 13:
- # 1824535827869, 14161747729169, 60628028874089, 67754204383529, 81240600887759, 93595283908439
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