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%I #14 Jul 29 2023 21:48:16
%S 3,5,7,113,397,577,7573,14561,58543,100019,123407,136559,208283,
%T 210761,457871,608347,636043
%N Numbers k such that (7^k - 5^k)/2 is prime.
%C All terms are primes.
%C No other terms less than 10^5. - _Robert Price_, May 28 2012
%C No other terms less than 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=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
%o (PARI) is(n)=isprime((7^n-5^n)/2) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A062572, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. 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(7)-a(9) from _Robert Price_, May 28 2012
%E a(10)-a(17) from _Jon Grantham_, Jul 29 2023
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