A128344 Numbers k such that (7^k - 5^k)/2 is prime.

3, 5, 7, 113, 397, 577, 7573, 14561, 58543, 100019, 123407, 136559, 208283, 210761, 457871, 608347, 636043

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

No other terms less than 10^5. - Robert Price, May 28 2012

No other terms less than 10^6. - Jon Grantham, Jul 29 2023

Links

• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Cf. A062572, A128345, A128346, A128347, A128348, 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=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((7^n-5^n)/2) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(9) from Robert Price, May 28 2012

a(10)-a(17) from Jon Grantham, Jul 29 2023