A180741 Numbers k such that 5^k + 3^k - 1 is prime.

1, 3, 9, 39, 165, 11289, 44979, 192321, 377865

Offset: 1

Author

Vincenzo Librandi, Jan 22 2011

Keywords

• nonn
• more

Comments

No additional terms up to 5000. - Harvey P. Dale, Feb 01 2011

No additional terms up to 1000000. - Jon Grantham, Jul 29 2023

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. A155603.

Programs

Magma

[n: n in [0..1000]|IsPrime(5^n+3^n-1)]

Mathematica

Select[Range[5000],PrimeQ[5^#+3^#-1]&]  (* Harvey P. Dale, Feb 01 2011 *)

PARI

is(n)=ispseudoprime(5^n+3^n-1) \\ Charles R Greathouse IV, Jun 13 2017

Python

from sympy import isprime
def afind(limit, startk=1):
    pow5, pow3 = 5**startk, 3**startk
    for k in range(startk, limit+1):
        if isprime(pow5 + pow3 - 1): print(k, end=", ")
        pow5 *= 5; pow3 *= 3
afind(1000) # Michael S. Branicky, Aug 21 2021

Extensions

a(6) from Michael S. Branicky, Aug 21 2021

a(7) from Michael S. Branicky, May 13 2023

a(8), a(9) from Jon Grantham, Jul 29 2023