A095737 Numbers k such that 2^k-1 is divisible by abs(p^2-k^2-1) for some prime p.

2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset

1,1

Comments

Previous name: Mersenne-like sequence factors of complex real square type 2*Prime[m]^2-n^2-1.

Includes all the primes, since for a prime q, 2^p-1 is divisible by abs(p^2-k^2-1) = 1 when p = q. - Amiram Eldar, Jun 07 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..84

Mathematica

q[n_] := AnyTrue[Divisors[2^n-1], PrimeQ[Sqrt[Abs[# - n^2 - 1]]] &]; Select[Range[150], q] (* Amiram Eldar, Jun 07 2025 *)

Crossrefs

Cf. A000225, A095735.

Sequence in context: A324697 A082664 A342008 * A054022 A185603 A046654

Adjacent sequences: A095734 A095735 A095736 * A095738 A095739 A095740

Keyword

nonn

Author

Roger L. Bagula, Jul 06 2004

Extensions

New name from Amiram Eldar, Jun 07 2025

Status

approved