cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A100289 Numbers k such that (1!)^2 + (2!)^2 + (3!)^2 + ... + (k!)^2 is prime.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 10, 18, 21, 42, 51, 91, 133, 177, 182, 310, 3175, 9566, 32841
Offset: 1

Views

Author

T. D. Noe, Nov 11 2004 and Dec 11 2004

Keywords

Comments

All k <= 310 yield provable primes.
Write the sum as S(2,k)-1, where S(m,k) = Sum_{i=0..k} (i!)^m. Let p=1248829. Because p divides S(2,p-1)-1, p divides S(2,k)-1 for all k >= p-1. Hence there are no primes for k >= p-1.

Crossrefs

Cf. A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2).
Cf. A061062 ((0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2).
Cf. A289947 (k!^6), A290014 (k!^10).
Cf. also A104344.

Programs

Extensions

a(18) from T. D. Noe, Feb 15 2006
a(19) from Serge Batalov, Jul 29 2017