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%I #45 Dec 20 2023 10:00:11
%S 2,5,7,13,19,37,59,67,79,307,331,599,1301,12263,12589,18443,20149,
%T 27983,281807,656657,795829,832151
%N Numbers k such that (5^k - 2^k)/3 is prime.
%C No other terms less than 100000. - _Robert Price_, Apr 06 2012
%C All terms are primes. Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019
%C No other terms less than 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.
%e a(1)=2 because (5^2 - 2^2)/3 = (25 - 4)/3 = 7 is a prime.
%o (PARI) forprime(p=2,1e4,if(ispseudoprime((5^p-2^p)/3),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 16 2011
%K more,nonn
%O 1,1
%A _Hugo Pfoertner_, May 22 2003, Jun 23 2003
%E a(17) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 03 2007
%E a(18) from _David Radcliffe_, May 28 2007
%E a(19)-a(22) from _Jon Grantham_, Jul 29 2023
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