A082182 Numbers k such that (5^k - 2^k)/3 is prime.

2, 5, 7, 13, 19, 37, 59, 67, 79, 307, 331, 599, 1301, 12263, 12589, 18443, 20149, 27983, 281807, 656657, 795829, 832151

Offset

1,1

Comments

No other terms less than 100000. - Robert Price, Apr 06 2012

All terms are primes. Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

No other terms less than 1000000. - Jon Grantham, Jul 29 2023

Links

Table of n, a(n) for n=1..22.

OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b).

Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Example

a(1)=2 because (5^2 - 2^2)/3 = (25 - 4)/3 = 7 is a prime.

Prog

(PARI) forprime(p=2, 1e4, if(ispseudoprime((5^p-2^p)/3), print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

Crossrefs

Sequence in context: A175075 A262392 A056985 * A032719 A334246 A275287

Adjacent sequences: A082179 A082180 A082181 * A082183 A082184 A082185

Keyword

more,nonn

Author

Hugo Pfoertner, May 22 2003, Jun 23 2003

Extensions

a(17) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 03 2007

a(18) from David Radcliffe, May 28 2007

a(19)-a(22) from Jon Grantham, Jul 29 2023

Status

approved