A128071 Numbers k such that (3^k + 13^k)/16 is prime.

3, 7, 127, 2467, 3121, 34313

Offset: 1

Author

Alexander Adamchuk, Feb 14 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(4) is certified prime by primo; a(5) is a probable prime. - Ray G. Opao, Aug 02 2007

a(7) > 10^5. - Robert Price, Apr 14 2013

Crossrefs

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.

Programs

Mathematica

k=13; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

PARI

is(n)=isprime((3^n+13^n)/16) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

One more term from Ray G. Opao, Aug 02 2007

a(6) from Robert Price, Apr 14 2013