A118813 Primes of the form (2n)! - n! - 1.

3628679, 87178286159, 20922789847679, 265252859812191058635000805631999

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

Keywords

• nonn

Comments

The term a(7) (2407 digits) is too large to include even in the b-file.

All the numbers end in 9.

For all n, (2n)! - n! - 1 has exactly A027868(n) trailing 9s. - Rick L. Shepherd, Feb 16 2014

Generated by n = 5, 7, 8, 15, 103, 179, .... - R. J. Mathar, Sep 20 2012 (now A238011)

Examples

			For n=5, (2*5)! - 5! - 1 = 3628800 - 120 - 1 = 3628679, which is prime.
		

References

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

Links

• Rick L. Shepherd, Table of n, a(n) for n = 1..6

Crossrefs

Cf. A238011 (corresponding n), A118812, A237443.

Programs

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);