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%I #15 Mar 11 2023 23:06:54
%S 7,31,41,269,283,7333,8803
%N Numbers k such that (13^k - 3^k)/10 is prime.
%C All terms are primes.
%C No other terms exist < 100000.
%t k=10; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
%o (PARI) is(n)=isprime((13^n-3^n)/10) \\ _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, A128025, A128026, A128027, A128029, A128030, A128031, A128032.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 11 2007
%E One more term from _Farideh Firoozbakht_, Apr 03 2007
%E a(7)=8803 from _Robert Price_, Aug 12 2011
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