A298566 - OEIS

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.

%I #18 Apr 28 2020 16:36:04

%S 11,31,41,41,139,211,113,199,211,617,433,1093,379,1381,929,2381,3907,

%T 2851,1901,1051,2927,2347,3889,2251,2887,3943,2017,2089,4861,2357,

%U 7457,8317,8467,6091,8317,3331,7829,17707,8081,7873,16927,17029,15797,13411,17987,41737,12241

%N 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.

%C Greater than A298565.

%H Jeremy F. Alm, <a href="/A298566/a298566.ipynb.txt">Python program</a>

%H Jeremy F. Alm, <a href="https://arxiv.org/abs/1902.10046">Arithmetic Progressions of Length Three in Multiplicative Subgroups of F_p</a>, arXiv:1902.10046 [math.NT], 2019. Also in <a href="http://math.colgate.edu/~integers/u8/u8.Abstract.html">Integers</a> (2020) Vol. 20A, Article #A1.

%Y Cf. A298565.

%K nonn

%O 2,1

%A _Jeremy F. Alm_, Jan 21 2018