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

3, 7, 127, 2467, 3121, 34313

Offset

1,1

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

Links

Table of n, a(n) for n=1..6.

Mathematica

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

Prog

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

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.

Sequence in context: A042329 A125956 A260642 * A079622 A182330 A005844

Adjacent sequences: A128068 A128069 A128070 * A128072 A128073 A128074

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 14 2007

Extensions

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

a(6) from Robert Price, Apr 14 2013

Status

approved