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%I #17 Jun 13 2021 03:21:55
%S 3,7,71,251,1429,2131,2689,36683,60763
%N Numbers k such that (3^k + 14^k)/17 is prime.
%C All terms are primes.
%C a(10) > 10^5. - _Robert Price_, Apr 20 2013
%t k=14; 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+14^n)/17) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
%Y Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
%Y Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
%Y Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128073, A128074, A128075.
%Y Cf. A059801 (numbers k such that 4^k - 3^k is prime).
%Y Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
%Y Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 14 2007
%E 3 more terms from _Ryan Propper_, Jan 28 2008
%E a(8)-a(9) from _Robert Price_, Apr 20 2013
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