A100015 Subfactorial primes: primes of the form !k + 1 or !k - 1. Subfactorial or rencontres numbers or derangements !k = A000166(k).

2, 3, 43, 481066515733, 130850092279663

Offset: 1

Author

Jonathan Vos Post, Nov 18 2004

Keywords

• nonn

Comments

No additional terms through k <= 2000. - Harvey P. Dale, Feb 17 2023

Examples

			a(1) = 2 because !0 = !2 = 1, so !0 + 1 = !2 + 1 = 2.
a(5) = 130850092279663 because the 5th subfactorial prime is !17 - 1 = 130850092279664 - 1 = 130850092279663.
		

References

• R. A. Brualdi and H. J. Ryser: Combinatorial Matrix Theory, 1992, Section 7.2, p. 202.
• H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 23.

Links

• R. M. Dickau, Derangement diagrams.
• H. Fripertinger, The Recontre Numbers, an online calculator.
• Mehdi Hassani, Derangements and Applications, Journal of Integer Sequences, Vol. 6 (2003), #03.1.2

Crossrefs

Cf. A000166.

Programs

Mathematica

Select[Union[Flatten[Table[Subfactorial[n]+{1,-1},{n,20}]]],PrimeQ] (* Harvey P. Dale, Feb 17 2023 *)