A237580 -id:A237580 - cp's OEIS frontend

A237579 Least prime factor of (2n)! - n! + 1 (= A237580(n)).

2, 23, 5, 59, 7, 59, 87178286161, 29, 11, 443, 13, 587, 403291461126605629356979201, 3307, 17, 43, 19, 131, 83, 2791, 23, 113, 5502622159812088949850305428800254867109635014075023360001, 659, 761, 6108689, 29, 233, 31, 67, 181, 25649409970727, 1561016461, 151, 37, 223, 53, 139, 41, 29209, 43, 61

Offset: 1

M. F. Hasler, Feb 09 2014

nonn

For n=0 the expression equals 1 and has no prime factor at all.

The larger terms, and/or those ending in ...01, correspond to indices (listed in A237443) for which the expression itself is a prime (listed in A118812).

Kellen Shenton, Table of n, a(n) for n = 1..82

Cf. A237580, A237443, A118812.

PARI
```
n -> factor((2*n)!-n!+1)[1,1]
```

a(26)-a(42) from Chai Wah Wu, Oct 15 2019

Typo in a(32) corrected by Seth A. Troisi, May 13 2022

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

Original entry on oeis.org

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

cp's OEIS Frontend

A237579 Least prime factor of (2n)! - n! + 1 (= A237580(n)).

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

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