This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350702 #38 Aug 28 2023 08:20:49
%S A350702 929,1433,2393,2609,2657,4373,4793,6029,7529,10133,10433,10949,10973,
%T A350702 13049,13109,16829,18869,20873,22349,23417,24137,26717,27737,27893,
%U A350702 28433,28517,30977,33809,33857,37217,38189,38237,39209,39749,41453,41813,42569,43313,43613
%N A350702 Primes p such that 14*p + 1 divides 2^p - 1.
%C A350702 Known divisors of Mersenne(p) (2^p-1 or Mp for short) are of the form 2*k*p+1. See crossrefs for other k's. If k == 2 (mod 4), there are no such divisors in general. Here k is 14/2 = 7.
%H A350702 Karl-Heinz Hofmann, <a href="/A350702/a350702_1.txt">Mersenne(p) table with k = 7 and, if they exist, additional k < 7 plus their corresponding factors</a>.
%H A350702 mersenne.ca, <a href="https://www.mersenne.ca/exponent/10973">a(13) = M10973 Mersenne number exponent details</a>.
%H A350702 mersenne.ca, <a href="https://www.mersenne.ca/k/7/3/2000000">a(1..995) at GIMPS with k = 7 and Exponent 3..2000000</a>.
%F A350702 {p = A000040(i): 14*p+1 | A001348(i)}.
%e A350702 See LINKS for example of a(13).
%t A350702 Select[Range[45000], PrimeQ[#] && PowerMod[2, #, 14*# + 1] == 1 &] (* _Amiram Eldar_, Jan 27 2022 *)
%o A350702 (PARI) forprime(p=1, 1e6, if (Mod(2, p*14+1)^p==1, print1(p,", ")))
%o A350702 (Python) from sympy import sieve
%o A350702 print([p for p in sieve[1:1000000] if pow(2, p, 14*p+1) == 1])
%Y A350702 Cf. A002515 (k = 1), A188130 (k = 3), A122095 (k = 4), A188133 (k = 5).
%Y A350702 Cf. A000040, A001348.
%K A350702 nonn
%O A350702 1,1
%A A350702 _Karl-Heinz Hofmann_, Jan 27 2022