A237579 -id:A237579 - cp's OEIS frontend

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

2, 23, 87178286161, 403291461126605629356979201, 5502622159812088949850305428800254867109635014075023360001

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

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

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

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

Cf. A237443 (corresponding values of n).

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);

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

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

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

A237580 a(n) = (2n)! - n! + 1.

Original entry on oeis.org

1, 2, 23, 715, 40297, 3628681, 479000881, 87178286161, 20922789847681, 6402373705365121, 2432902008173011201, 1124000727777567763201, 620448401733238960358401, 403291461126605629356979201, 304888344611713860414325708801, 265252859812191058635000805632001

Offset: 0

M. F. Hasler, Feb 09 2014

nonn

Primes are listed in A118812, the corresponding indices in A237443; the least prime factor of a(n) in A237579.

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Cf. A000142 (n!), A010050 ((2n)!)

[Factorial(2*n)-Factorial(n)+1: n in [0..15]]; // Vincenzo Librandi, Feb 11 2014

Table[((2 n)! - n! + 1), {n, 0, 30}] (* Vincenzo Librandi, Feb 11 2014 *)

PARI
```
A237580 = n->(2*n)!-n!+1
```

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Programs

Maple

Mathematica

PARI

Formula