login
A128345
Numbers k such that (8^k - 5^k)/3 is prime.
19
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
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
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