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%I #33 Jul 29 2023 20:52:29
%S 1,3,9,39,165,11289,44979,192321,377865
%N Numbers k such that 5^k + 3^k - 1 is prime.
%C No additional terms up to 5000. - _Harvey P. Dale_, Feb 01 2011
%C No additional terms up to 1000000. - _Jon Grantham_, Jul 29 2023
%H Jon Grantham and Andrew Granville, <a href="https://arxiv.org/abs/2307.07894">Fibonacci primes, primes of the form 2^n-k and beyond</a>, arXiv:2307.07894 [math.NT], 2023.
%t Select[Range[5000],PrimeQ[5^#+3^#-1]&] (* _Harvey P. Dale_, Feb 01 2011 *)
%o (Magma) [n: n in [0..1000]|IsPrime(5^n+3^n-1)]
%o (PARI) is(n)=ispseudoprime(5^n+3^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017
%o (Python)
%o from sympy import isprime
%o def afind(limit, startk=1):
%o pow5, pow3 = 5**startk, 3**startk
%o for k in range(startk, limit+1):
%o if isprime(pow5 + pow3 - 1): print(k, end=", ")
%o pow5 *= 5; pow3 *= 3
%o afind(1000) # _Michael S. Branicky_, Aug 21 2021
%Y Cf. A155603.
%K nonn,more
%O 1,2
%A _Vincenzo Librandi_, Jan 22 2011
%E a(6) from _Michael S. Branicky_, Aug 21 2021
%E a(7) from _Michael S. Branicky_, May 13 2023
%E a(8), a(9) from _Jon Grantham_, Jul 29 2023