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

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

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

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

• 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, 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.

Programs

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 *)

PARI

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

Extensions

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

a(8) from Jon Grantham, Jul 29 2023