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

3,5

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.

Formula

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

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 *)

Crossrefs

Cf. A006882, A007911.

Sequence in context: A209349 A242095 A336169 * A019755 A085475 A211399

Adjacent sequences: A007909 A007910 A007911 * A007913 A007914 A007915

Keyword

nonn,easy,nice

Author

J. H. Conway

Status

approved