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

1,1

Comments

All terms are primes. No other terms < 1000000.

Links

Table of n, a(n) for n=1..13.

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A028491, A057468, A059801, A121877.

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

Sequence in context: A215487 A146037 A172514 * A245723 A118128 A113875

Adjacent sequences: A128021 A128022 A128023 * A128025 A128026 A128027

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 11 2007

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

Status

approved