A128354 Numbers k such that (19^k - 5^k)/14 is prime.

5, 17, 31, 59, 373, 643, 2843, 5209, 85009

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(10) > 10^5. - Robert Price, Jul 22 2013

Crossrefs

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

Cf. A004061, A082182, A121877, A059802.

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

Programs

Mathematica

k=19; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((19^n-5^n)/14) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(9) from Robert Price, Jul 22 2013