Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Jul 29 2023 21:49:10
%S 2,3,7,19,31,67,89,9227,43891,854149
%N Numbers k such that (8^k - 3^k)/5 is prime.
%C All terms are primes.
%C Verified the first 8 terms in sequence. Also, the next number in the sequence, if one exists is > 43691. - _Robert Price_, Mar 16 2010
%C a(10) > 10^5. - _Robert Price_, Jul 27 2011
%C a(11) > 10^6. - _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 k=5; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
%o (PARI) is(n)=isprime((8^n-3^n)/5) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 11 2007
%E 9227 from _Farideh Firoozbakht_, Apr 08 2007
%E a(9) from _Robert Price_, Jul 27 2011
%E a(10) from _Jon Grantham_, Jul 29 2023