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