A081762 Primes p such that p*(p-2) divides 2^(p-1)-1.

3, 5, 17, 37, 257, 457, 1297, 2557, 4357, 6481, 8009, 11953, 26321, 44101, 47521, 47881, 49681, 57241, 65537, 74449, 84421, 97813, 141157, 157081, 165601, 225457, 278497, 310591, 333433, 365941, 403901, 419711, 476737, 557041, 560737, 576721, 1011961, 1033057

Offset: 1

Author

Benoit Cloitre, Apr 09 2003

Keywords

• easy
• nonn

Comments

Primes p such that p-2 divides 2^(p-1) - 1. The only member in A006512 is 5. - Robert Israel, Dec 03 2014

N=647089 is the smallest composite number such that (n-1)^2-1 divides 2^(n-1)-1. - M. F. Hasler, Jul 24 2015

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1076 (first 303 terms from Chai Wah Wu)

Programs

Maple

select(p -> isprime(p) and 2 &^ (p-1) - 1  mod (p-2) = 0, [seq(2*i+1,i=1..10^6)]);  # Robert Israel, Dec 03 2014

Mathematica

Select[Prime[Range[2,81000]],PowerMod[2,#-1,#(#-2)]==1&] (* Harvey P. Dale, Sep 11 2023 *)

PARI

lista(nn) = {forprime(p = 3, nn, if (! ((2^(p-1)-1) % (p*(p-2))), print1(p, ", "));)} \\ Michel Marcus, Dec 02 2013

Python

from sympy import prime
from gmpy2 import powmod
A081762_list = [p for p in (prime(n) for n in range(2,10**5)) if powmod(2,p-1,p*(p-2)) == 1] # Chai Wah Wu, Dec 03 2014

Extensions

More terms from Michel Marcus, Dec 02 2013