A128882 a(n) = n!! - 1.

0, 0, 1, 2, 7, 14, 47, 104, 383, 944, 3839, 10394, 46079, 135134, 645119, 2027024, 10321919, 34459424, 185794559, 654729074, 3715891199, 13749310574, 81749606399, 316234143224, 1961990553599, 7905853580624, 51011754393599

Offset: 0

Author

Alexander Adamchuk, Apr 18 2007

Keywords

• nonn

Comments

n divides a(n-1) and a(n+1) for n = {1, 2, 8, 11, 16, 19, 23, 31, 32, 43, 64, 67, 71, ...} which include all powers of 2 except 2^2 and some odd primes of the form 4k+3 belonging to A002145.

p^2 divides a(p-1) for odd prime p = 71.

p^2 divides a(p+1) for odd prime p = 23.

a(n) is prime for n = {3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, ...} = A007749; A007749(n) = 2*A091415(n-1) for n > 1. Corresponding primes of the form n!! - 1 are listed in A117141, cf. also A093173.

Links

• Eric Weisstein's World of Mathematics, Double Factorial

Crossrefs

Cf. A006882, A002145, A117141, A093173, A007749, A091415.

Programs

Mathematica

Table[ n!! - 1, {n,0,35} ]

Formula

a(n) = A006882(n) - 1.