A352347 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.

5, 31, 29, 89, 11, 11, 13, 89, 7, 283, 29, 211, 13, 643, 2711, 491, 1627, 1699, 283, 727, 1493, 1663, 37, 89, 907, 1039, 73, 571, 2707, 149, 179, 197, 443, 463, 1187, 4133, 383, 359, 251, 1567, 4603, 3469, 2069, 313, 677, 1319, 2441, 647, 3733, 3623, 31, 1447

Offset: 1

Author

Robert G. Wilson v, Mar 14 2022

Keywords

• nonn

Comments

Inspired by A350964.

In the first 100000 terms, greatest prime encountered was 204114067.

Records: 5, 31, 89, 283, 643, 2711, 4133, 4603, 8317, 23561, 25819, 45083, ...

Examples

			a(1) = 5 since A001132(1) | 2^5 - 5^2 = 32 - 25 = 7.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000
• Robert G. Wilson v, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A001132, A350964.

Programs

PARI

f(q) = forprime(p=5, oo, if(Mod(2, q)^p == Mod(p, q)^2, return(p)));
lista(nn) = forprime(q=7, nn, if((q+2)%8<4, print1(f(q), ", "))); \\ Jinyuan Wang, Jul 14 2022

Extensions

Name edited by Jinyuan Wang, Jul 14 2022