%I #39 Jul 16 2022 01:07:24
%S 5,31,29,89,11,11,13,89,7,283,29,211,13,643,2711,491,1627,1699,283,
%T 727,1493,1663,37,89,907,1039,73,571,2707,149,179,197,443,463,1187,
%U 4133,383,359,251,1567,4603,3469,2069,313,677,1319,2441,647,3733,3623,31,1447
%N Least odd prime p such that q divides 2^p - p^2, where q is n-th prime of the form 8*k +- 1, or -1 if no such prime exists.
%C Inspired by A350964.
%C In the first 100000 terms, greatest prime encountered was 204114067.
%C Records: 5, 31, 89, 283, 643, 2711, 4133, 4603, 8317, 23561, 25819, 45083, ...
%H Robert G. Wilson v, <a href="/A352347/b352347.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert G. Wilson v, <a href="/A352347/a352347.txt">Table of n, a(n) for n = 1..100000</a>
%e a(1) = 5 since A001132(1) | 2^5 - 5^2 = 32 - 25 = 7.
%o (PARI) f(q) = forprime(p=5, oo, if(Mod(2, q)^p == Mod(p, q)^2, return(p)));
%o lista(nn) = forprime(q=7, nn, if((q+2)%8<4, print1(f(q), ", "))); \\ _Jinyuan Wang_, Jul 14 2022
%Y Cf. A001132, A350964.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Mar 14 2022
%E Name edited by _Jinyuan Wang_, Jul 14 2022