A128342 Numbers k such that (13^k + 5^k)/18 is prime.

13, 19, 31, 359, 487, 757, 761, 1667, 2551, 3167, 6829

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

No other terms below 23600. - Max Alekseyev, Feb 01 2010

a(12) > 10^5. - Robert Price, Apr 30 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

Mathematica

k=13; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((13^n+5^n)/18) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

Four more terms from Max Alekseyev, Feb 01 2010