A100599 Numbers k such that (prime(k)-1)! + prime(k)^7 is prime.

7, 14, 16, 59

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 k-th prime.

Example

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

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+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 * A353440 A198390 A118905

Adjacent sequences: A100596 A100597 A100598 * A100600 A100601 A100602

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Nov 30 2004

Status

approved