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%I #14 Nov 01 2018 21:39:07
%S 3,7,127,2467,3121,34313
%N Numbers k such that (3^k + 13^k)/16 is prime.
%C All terms are primes.
%C a(4) is certified prime by primo; a(5) is a probable prime. - _Ray G. Opao_, Aug 02 2007
%C a(7) > 10^5. - _Robert Price_, Apr 14 2013
%t k=13; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]
%o (PARI) is(n)=isprime((3^n+13^n)/16) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128069, A128070, A128072, A128073, A128074, A128075. 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, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 14 2007
%E One more term from _Ray G. Opao_, Aug 02 2007
%E a(6) from _Robert Price_, Apr 14 2013
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