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

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

Offset

1,2

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

Table of n, a(n) for n=1..9.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A155603.

Sequence in context: A149026 A149027 A330795 * A121101 A280066 A360876

Adjacent sequences: A180738 A180739 A180740 * A180742 A180743 A180744

Keyword

nonn,more

Author

Vincenzo Librandi, Jan 22 2011

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

Status

approved