A128348 Numbers k such that (12^k - 5^k)/7 is prime.

2, 3, 31, 41, 53, 101, 421, 1259, 4721, 45259

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

Primality of the primes formed by a(8) and a(9) were certified by Primo. - Ray G. Opao, Jul 01 2012

a(11) > 10^5. - Robert Price, Mar 02 2013

Crossrefs

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

Cf. A004061, A082182, A121877, A059802.

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

Mathematica

k=12; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((12^n-5^n)/7) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8) and a(9) from Ray G. Opao, Jul 01 2012

a(10) from Robert Price, Mar 02 2013