

A100599


Numbers k such that (prime(k)1)! + prime(k)^7 is prime.


2




OFFSET

1,1


COMMENTS

k = {7, 14, 16, 59} yields primes p(k) = {17, 43, 53, 277}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(5) > 600.  Jinyuan Wang, Apr 10 2020


LINKS

Table of n, a(n) for n=1..4.


FORMULA

Numbers k such that (prime(k)1)! + prime(k)^7 is prime, where prime(k) is the kth prime.


EXAMPLE

a(7) = 7 because (prime(7)1)! + prime(7)^7 = (171)! + 17^7 = 20923200226673 is the smallest prime of that form.


MATHEMATICA

lst={}; Do[p=Prime[n]; If[PrimeQ[(p1)!+p^7], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)


PROG

(PARI) is(k) = ispseudoprime((prime(k)1)! + prime(k)^7); \\ Jinyuan Wang, Apr 10 2020


CROSSREFS

Cf. A100598, A100600, A100858.
Sequence in context: A269173 A167197 A336797 * A198390 A118905 A254064
Adjacent sequences: A100596 A100597 A100598 * A100600 A100601 A100602


KEYWORD

nonn,hard,more


AUTHOR

Jonathan Vos Post, Nov 30 2004


STATUS

approved



