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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 A298566 #18 Apr 28 2020 16:36:04
%S A298566 11,31,41,41,139,211,113,199,211,617,433,1093,379,1381,929,2381,3907,
%T A298566 2851,1901,1051,2927,2347,3889,2251,2887,3943,2017,2089,4861,2357,
%U A298566 7457,8317,8467,6091,8317,3331,7829,17707,8081,7873,16927,17029,15797,13411,17987,41737,12241
%N 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.
%C A298566 Greater than A298565.
%H A298566 Jeremy F. Alm, <a href="/A298566/a298566.ipynb.txt">Python program</a>
%H A298566 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 A298566 Cf. A298565.
%K A298566 nonn
%O A298566 2,1
%A A298566 _Jeremy F. Alm_, Jan 21 2018