A128345 Numbers k such that (8^k - 5^k)/3 is prime.

2, 19, 1021, 5077, 34031, 46099, 65707, 347437

Offset

1,1

Comments

All terms are primes.

No further terms up to 5000 - Harvey P. Dale, Mar 23 2011

a(8) > 10^5 - Robert Price, Dec 22 2012

a(9) > 10^6 - Jon Grantham, Jul 29 2023

Links

Table of n, a(n) for n=1..8.

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

Mathematica

k=8; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 200}]
Select[Range[5000], PrimeQ[(8^#-5^#)/3]&]  (* Harvey P. Dale, Mar 23 2011 *)

Prog

(PARI) is(n)=isprime((8^n-5^n)/3) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A062572, A128344, 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: A024228 A015191 A165937 * A013052 A012956 A012976

Adjacent sequences: A128342 A128343 A128344 * A128346 A128347 A128348

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 27 2007

Extensions

a(4)-a(7) from Robert Price, Dec 22 2012

a(8) from Jon Grantham, Jul 29 2023

Status

approved