A128339 Numbers k such that (9^k + 5^k)/14 is prime.

3, 5, 13, 17, 43, 127, 229, 277, 6043, 11131, 11821

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(12) > 10^5. - Robert Price, Dec 26 2012

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128340, A128341, A128342, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

Magma

[n: n in [3..300] |IsPrime((9^n + 5^n) div 14)]; // Vincenzo Librandi, Nov 02 2018

Mathematica

k=9; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((9^n+5^n)/14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

3 more PRP terms from Sean A. Irvine, Oct 01 2009