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A128882 a(n) = n!! - 1. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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
FORMULA
a(n) = A006882(n) - 1.
MATHEMATICA
Table[ n!! - 1, {n, 0, 35} ]
CROSSREFS
Sequence in context: A018542 A018577 A121118 * A018281 A018592 A123752
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Apr 18 2007
STATUS
approved

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Last modified May 26 15:05 EDT 2024. Contains 372826 sequences. (Running on oeis4.)