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

2, 3, 43, 481066515733, 130850092279663

Offset

1,1

Comments

No additional terms through n <= 2000. (* Harvey P. Dale, Feb 17 2023 *)

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

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

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

Example

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

Mathematica

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

Crossrefs

Cf. A000166.

Sequence in context: A062581 A077520 A230061 * A317672 A352003 A356047

Adjacent sequences: A100012 A100013 A100014 * A100016 A100017 A100018

Keyword

nonn

Author

Jonathan Vos Post, Nov 18 2004

Status

approved