A089920 Indices of primes p such that 7^p - 2 is prime.

1, 4, 11, 149

Offset

1,2

Comments

Except for p=2, 2, 5^p - 2 cannot be prime. This immediately follows from the fact that a number N = (3k+2)^p - 2 cannot be prime for p > 2 because N = 3H + 2^p - 2 = 3H + 2(2^(p-1)-1) is divisible by 3.

a(5) > 8742, if it exists (cf. J.W.L. (Jan) Eerland's comment in A147782). - Amiram Eldar, Jul 07 2024

a(5) > 23967, if it exists (using A090669). - Michael S. Branicky, Aug 17 2024

Links

Table of n, a(n) for n=1..4.

Formula

a(n) = A000720(A147782(n)). - Amiram Eldar, Jul 07 2024

Mathematica

Select[Range[500], PrimeQ[7^Prime[#]-2]&] (* Harvey P. Dale, May 02 2011 *)
Position[Prime[Range[150]], _?(PrimeQ[7^#-2]&)]//Flatten (* Harvey P. Dale, May 11 2016 *)

Prog

(PARI) forprime(p=2, 1e4, if(ispseudoprime(7^p-2), print1(x", ")))

Crossrefs

Cf. A147782 (primes p such that 7^p - 2 is prime), A000720, A090669.

Sequence in context: A018242 A006248 A119571 * A303881 A305277 A118197

Adjacent sequences: A089917 A089918 A089919 * A089921 A089922 A089923

Keyword

nonn,more

Author

Cino Hilliard, Jan 11 2004

Extensions

Definition clarified by Harvey P. Dale, May 02 2011.

Status

approved