A128030 - OEIS

%I #17 Mar 11 2023 23:06:50

%S 2,3,31,467,1747,29683

%N Numbers k such that (16^k - 3^k)/13 is prime.

%C All terms are primes.

%C No other terms < 100000.

%t k=13; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

%o (PARI) is(n)=isprime((16^n-3^n)/13) \\ _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, A128028, A128029, A128031, A128032.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Feb 11 2007

%E 1747 from _Farideh Firoozbakht_, Apr 08 2007

%E a(6)=29683 from _Robert Price_, Sep 13 2011