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%I #39 Jul 29 2023 20:53:18
%S 13,19,23,31,47,127,223,281,2083,5281,7411,7433,19051,27239,35863,
%T 70327,128941,147571,182099,866029
%N Numbers k such that (5^k - 3^k)/2 = A005059(k) is prime.
%C All terms are primes. Their indices are listed in A123704.
%C Corresponding primes are listed in A123705.
%C If it exists, a(17) > 125000. - _Robert Price_, Aug 15 2011
%C If it exists, a(21) > 1000000. - _Jon Grantham_, Jul 29 2023
%H OEIS Wiki, <a href="http://oeis.org/wiki/Primes_of_the_form_(a%5En%2Bb%5En)/(a%2Bb)_and_(a%5En-b%5En)/(a-b)">Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)</a>.
%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.
%F a(n) = prime(A123704(n)).
%t Do[f=(5^n-3^n)/2;If[PrimeQ[f],Print[{n,f}]],{n,1,300}]
%o (PARI) forprime(p=2,1e4,if(ispseudoprime((5^p-3^p)>>1),print1(p", "))) \\ _Charles R Greathouse IV_, Jun 16 2011
%Y Cf. A005058, A005059, A109347, A120612, A081186, A121824, A123704, A123705.
%K nonn,hard,more
%O 1,1
%A _Alexander Adamchuk_, Aug 31 2006, Oct 08 2006
%E More terms from _Farideh Firoozbakht_, Oct 11 2006
%E a(13)-a(16) from _Robert Price_, Aug 15 2011
%E a(17)-a(19) from _Kellen Shenton_, May 18 2022
%E a(20) from _Jon Grantham_, Jul 29 2023
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