A186193 Numbers n such that n!! is divisible by (n+1).

14, 20, 24, 26, 32, 34, 38, 44, 48, 50, 54, 56, 62, 64, 68, 74, 76, 80, 84, 86, 90, 92, 94, 98, 104, 110, 114, 116, 118, 120, 122, 124, 128, 132, 134, 140, 142, 144, 146, 152, 154, 158, 160, 164, 168, 170, 174, 176, 182, 184, 186, 188, 194, 200, 202, 204, 206

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

Cf. A006882, A119688.

Sequence in context: A193672 A087678 A144585 * A285426 A108874 A063848

Adjacent sequences: A186190 A186191 A186192 * A186194 A186195 A186196

Keyword

nonn

Author

Zak Seidov, Feb 14 2011

Status

approved