OFFSET
1,1
COMMENTS
Positions of zeros in A119688 (n!! mod (n+1)).
All terms are even (for n odd, n!! is odd and not divisible by even (n+1))
Apparently all integers of form 8+6k, k >= 1, are in the sequence.
Exactly all even numbers n >= 14 with composite n+1 are in this sequence. - Alois P. Heinz, Feb 15 2011
LINKS
Zak Seidov, Table of n, a(n) for n = 1..697
Eric Weisstein's World of Mathematics, Double Factorial
EXAMPLE
14!! = 14*12*10*8*6*4*2 = 645120 = 43008*15, so 14 is in the sequence.
16!! = 16*14*12*10*8*6*4*2 = 10321920 is not divisible by 17, so 16 is not in the sequence.
20!! = 20*18*16*14*12*10*8*6*4*2 = 3715891200 = 176947200*21, so 20 is in the sequence.
MAPLE
a:= proc(n) option remember; local k;
if n=1 then 14
else for k from 2+a(n-1) by 2
while isprime(k+1)
do od; k
fi
end:
seq(a(n), n=1..100); # Alois P. Heinz, Feb 15 2011
MATHEMATICA
Select[Range[300], Divisible[#!!, #+1]&] (* Jean-François Alcover, Nov 11 2020 *)
PROG
(Magma) DoubleFactorial:=func< n | &*[n..2 by -2] >; [ n: n in [1..250] | DoubleFactorial(n) mod (n+1) eq 0 ]; // Klaus Brockhaus, Feb 15 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Feb 14 2011
STATUS
approved