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A100599 Numbers k such that (prime(k)-1)! + prime(k)^7 is prime. 2
7, 14, 16, 59 (list; graph; refs; listen; history; text; internal format)
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 * A198390 A118905 A254064

Adjacent sequences:  A100596 A100597 A100598 * A100600 A100601 A100602

KEYWORD

nonn,hard,more

AUTHOR

Jonathan Vos Post, Nov 30 2004

STATUS

approved

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Last modified March 4 23:13 EST 2021. Contains 341812 sequences. (Running on oeis4.)