A298566 a(n) is the smallest prime q congruent to 1 mod n such that for all primes p >= q with p congruent to 1 mod n, the multiplicative subgroup H of (Z/pZ)* of index n contains a nontrivial mod-p arithmetic progression of length 3.
11, 31, 41, 41, 139, 211, 113, 199, 211, 617, 433, 1093, 379, 1381, 929, 2381, 3907, 2851, 1901, 1051, 2927, 2347, 3889, 2251, 2887, 3943, 2017, 2089, 4861, 2357, 7457, 8317, 8467, 6091, 8317, 3331, 7829, 17707, 8081, 7873, 16927, 17029, 15797, 13411, 17987, 41737, 12241
Offset: 2
Keywords
Links
- Jeremy F. Alm, Python program
- Jeremy F. Alm, Arithmetic Progressions of Length Three in Multiplicative Subgroups of F_p, arXiv:1902.10046 [math.NT], 2019. Also in Integers (2020) Vol. 20A, Article #A1.
Crossrefs
Cf. A298565.
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