A118812 Primes of the form (2n)! - n! + 1.

2, 23, 87178286161, 403291461126605629356979201, 5502622159812088949850305428800254867109635014075023360001

Offset

1,1

Comments

a(6) is a 41025-digit prime corresponding to n = 5666, and a(7) is a 288639-digit prime corresponding to n = 32918. See A237443 for additional values of n. - Kellen Shenton, Dec 21 2024

Primes in sequence A237580 = n -> (2n)! - n! + 1, i.e., the terms of that sequence which coincide with A237579(n) = least prime factor of (2n)! - n! + 1. - M. F. Hasler, Feb 09 2014

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 159.

Links

Table of n, a(n) for n=1..5.

Formula

A118812 = A237580 o A237443 = A237579 o A237443. - M. F. Hasler, Feb 09 2014

Example

For n=2, (2*2)! - 2! + 1 = 24 - 2 + 1 = 23, which is prime.

Maple

PFACT:=proc(N) local i, r; for i from 1 by 1 to N do r:=(2*i)!-i!+1; if isprime(r) then print(i); fi; od; end: PFACT(100);

Mathematica

Select[Table[(2n)!-n!+1, {n, 30}], PrimeQ] (* Harvey P. Dale, May 05 2018 *)

Prog

(PARI) for(n=1, 999, ispseudoprime(p=(2*n)!-n!+1)&&print1(p", ")) \\ M. F. Hasler, Feb 09 2014

Crossrefs

Cf. A237443 (corresponding values of n).

Sequence in context: A334616 A089987 A162605 * A228241 A054909 A171636

Adjacent sequences: A118809 A118810 A118811 * A118813 A118814 A118815

Keyword

nonn

Author

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

Status

approved