A344360 Primes p such that (2^p - 2)/p + 1 is prime.

2, 3, 5, 7, 13, 53, 67, 83, 167, 1367, 2473, 4789, 34127, 219217

Offset

1,1

Comments

a(15) > 1099997, if it exists. - Karl-Heinz Hofmann, Jul 27 2021

These are primes p such that 2^((2^p-2)/p) == 1 (mod (2^p-2)/p+1) if and only if there are no pseudoprimes of the form (2^q-2)/q+1 with q prime. - Thomas Ordowski, Aug 29 2021

Links

Table of n, a(n) for n=1..14.

Example

7 is a term because (2^7 - 2)/7 + 1 = 19 is prime.

Mathematica

Select[Prime@ Range[10^3], PrimeQ[(2^# - 2)/# + 1] &] (* Michael De Vlieger, Oct 12 2021 *)

Prog

(PARI) lista(lim)={forprime(p=1, lim, if(ispseudoprime((2^p-2)/p+1), print1(p, ", ")))}
(PARI) c3(p) = {s=3; for(x=1, p, s=(s^2)%((2^p-2)/p+1)); if(s==9, print1(p, ", "))} /* PRP Test */

Crossrefs

Cf. A064535, A344361.

Sequence in context: A038965 A295738 A265781 * A250407 A055694 A249797

Adjacent sequences: A344357 A344358 A344359 * A344361 A344362 A344363

Keyword

nonn,more

Author

Jorge Coveiro, May 15 2021

Extensions

a(14) from Karl-Heinz Hofmann, Jun 11 2021

Status

approved