login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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.
2
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
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
KEYWORD
nonn
AUTHOR
Jeremy F. Alm, Jan 21 2018
STATUS
approved