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

2,1

Comments

Greater than A298565.

Links

Table of n, a(n) for n=2..48.

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.

Sequence in context: A173972 A167488 A361976 * A090756 A038351 A068871

Adjacent sequences: A298563 A298564 A298565 * A298567 A298568 A298569

Keyword

nonn

Author

Jeremy F. Alm, Jan 21 2018

Status

approved