A128346 Numbers k such that (9^k - 5^k)/4 is prime.

3, 11, 17, 173, 839, 971, 40867, 45821, 147503

Offset

1,1

Comments

All terms are primes.

a(9) > 10^5. - Robert Price, Jan 19 2013

a(10) > 10^6. - Jon Grantham, Jul 29 2023

Links

Table of n, a(n) for n=1..9.

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

Mathematica

k=9; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]

Prog

(PARI) is(n)=isprime((9^n-5^n)/4) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A062572, A128344, A128345, 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: A072982 A124787 A080306 * A128031 A194128 A127995

Adjacent sequences: A128343 A128344 A128345 * A128347 A128348 A128349

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 27 2007

Extensions

a(7)-a(8) from Robert Price, Jan 19 2013

a(8) corrected by Robert Price, Jan 20 2013

a(9) from Jon Grantham, Jul 29 2023

Status

approved