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

Author

Hugo Pfoertner, May 22 2003, Jun 23 2003

Keywords

• more
• nonn

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

Examples

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

Links

• 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.

Programs

PARI

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

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