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

1,1

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

Table of n, a(n) for n=1..17.

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

Mathematica

k=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]

Prog

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

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.

Sequence in context: A046201 A374101 A292848 * A259385 A114366 A088092

Adjacent sequences: A128341 A128342 A128343 * A128345 A128346 A128347

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 27 2007

Extensions

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

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

Status

approved