OFFSET
1,2
COMMENTS
k = {1, 2, 4, 5, 8, 10} yields primes p(k) = {2, 3, 7, 11, 19, 29}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(7) > 600. - Jinyuan Wang, Apr 10 2020
a(7) > 900. - Tyler NeSmith, May 05 2021
a(7) > 2500. - Michael S. Branicky, Jul 03 2024
EXAMPLE
a(1) = 1 because (prime(1)-1)! + prime(1)^8 = (2-1)! + 2^8 = 257 is the smallest prime of that form.
a(5) = 8 because (prime(8)-1)! + prime(8)^8 = (19-1)! + 19^8 = 304888344611713861001750412961 is the 5th smallest prime of that form.
MATHEMATICA
lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^8], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
PROG
(PARI) is(k) = ispseudoprime((prime(k)-1)! + prime(k)^8); \\ Jinyuan Wang, Apr 10 2020
CROSSREFS
KEYWORD
nonn,hard,more,less
AUTHOR
Jonathan Vos Post, Nov 30 2004
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007
STATUS
approved