A128344 - OEIS

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

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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

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

KEYWORD

hard,more,nonn

AUTHOR

EXTENSIONS

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

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

STATUS

approved