A007912 Quantum factorials: (n-1)!! - (n-2)!! (mod n).

1, 1, 0, 1, 5, 1, 0, 1, 2, 3, 0, 1, 0, 1, 0, 9, 2, 15, 0, 1, 2, 9, 0, 1, 0, 7, 0, 15, 2, 1, 0, 1, 0, 27, 0, 1, 0, 25, 0, 21, 2, 11, 0, 1, 45, 33, 0, 25, 0, 39, 0, 27, 0, 49, 0, 1, 57, 15, 0, 1, 0, 1, 0, 33, 2, 51, 0, 35, 2, 9, 0, 1, 0, 19, 0, 39, 77, 65, 0, 1, 81, 63, 0, 1, 0, 33, 0, 45, 0

Offset: 3

Author

J. H. Conway

Keywords

• nonn
• easy
• nice

References

• S. P. Hurd and J. S. McCranie, Quantum factorials. Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). Congr. Numer. 104 (1994), 19-24.

Links

• T. D. Noe, Table of n, a(n) for n = 3..2000
• S. P. Hurd and J. S. McCranie, Quantum factorials, 1994.

Crossrefs

Cf. A006882, A007911.

Programs

Maple

a:= n-> (d-> irem(d(n-1)-d(n-2), n))(doublefactorial):
seq(a(n), n=3..100);  # Alois P. Heinz, Dec 17 2021

Mathematica

Table[Mod[(n-1)!!-(n-2)!!,n],{n,3,100}] (* Harvey P. Dale, Aug 07 2012 *)

Formula

a(n) = 0 iff n is odd and not a prime congruent to 3 modulo 4. - Charlie Neder, Feb 24 2019