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%I #22 Jul 29 2023 22:11:04
%S 2,19,1021,5077,34031,46099,65707,347437
%N Numbers k such that (8^k - 5^k)/3 is prime.
%C All terms are primes.
%C No further terms up to 5000 - _Harvey P. Dale_, Mar 23 2011
%C a(8) > 10^5 - _Robert Price_, Dec 22 2012
%C a(9) > 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=8; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,200}]
%t Select[Range[5000],PrimeQ[(8^#-5^#)/3]&] (* _Harvey P. Dale_, Mar 23 2011 *)
%o (PARI) is(n)=isprime((8^n-5^n)/3) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A062572, A128344, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
%Y Cf. A004061, A082182, A121877, A059802.
%Y Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 27 2007
%E a(4)-a(7) from _Robert Price_, Dec 22 2012
%E a(8) from _Jon Grantham_, Jul 29 2023
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