A128341 Numbers k such that (12^k + 5^k)/17 is prime.

3, 5, 13, 347, 977, 1091, 4861, 4967, 34679

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(10) > 10^5. - Robert Price, May 05 2013

Crossrefs

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128342, A128343.

Cf. A004061, A082182, A121877, A059802.

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Programs

Mathematica

k=12; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]
Select[Range[1100],PrimeQ[(12^#+5^#)/17]&] (* Harvey P. Dale, Jul 24 2012 *)

PARI

is(n)=isprime((12^n+5^n)/17) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

Two more terms (a(7) and a(8)) from Harvey P. Dale, Jul 24 2012

a(9) from Robert Price, May 05 2013