A128024 Numbers k such that (7^k - 3^k)/4 is prime.

3, 7, 19, 109, 131, 607, 863, 2917, 5923, 12421, 187507, 353501, 817519

Offset: 1

Author

Alexander Adamchuk, Feb 11 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes. No other terms < 1000000.

Links

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

Crossrefs

Cf. A028491, A057468, A059801, A121877.

Cf. A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

Mathematica

k=4; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

PARI

forprime(p=3,1e5,if(ispseudoprime((7^p-3^p)/4),print1(p", "))) \\ Charles R Greathouse IV, Jun 01 2011

Python

from sympy import isprime
def aupto(lim): return [k for k in range(lim+1) if isprime((7**k-3**k)//4)]
print(aupto(900)) # Michael S. Branicky, Mar 07 2021

Extensions

a(8)-a(9) from Farideh Firoozbakht, Apr 08 2007

a(10) from Robert Price, Jun 01 2011

a(11)-a(13) from Jon Grantham, Jul 29 2023