A205786 Least positive integer j such that n divides C(k)-C(j), where k, as in A205785, is the least number for which there is such a j, and C=A205825.

1, 1, 3, 4, 2, 2, 1, 4, 3, 2, 1, 4, 3, 7, 6, 2, 3, 2, 1, 5, 7, 4, 3, 6, 5, 2, 4, 8, 5, 6, 4, 8, 4, 8, 7, 4, 5, 5, 3, 6, 12, 7, 3, 6, 6, 6, 3, 8, 7, 5, 8, 2, 3, 4, 7, 8, 3, 5, 2, 6, 6, 4, 9, 8, 6, 4, 7, 8, 3, 7, 6, 9, 1, 5, 10, 9, 7, 6, 8, 8, 9, 12, 5, 8, 8, 9, 6, 6, 1, 6, 7, 6, 4, 11, 5, 8, 8

Offset: 1

Author

Clark Kimberling, Feb 01 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Examples

			1 divides C(2)-C(1) -> k=2, j=1;
2 divides C(3)-C(1) -> k=3, j=1;
3 divides C(4)-C(3) -> k=4, j=3;
4 divides C(5)-C(4) -> k=5, j=4;
5 divides C(4)-C(2) -> k=4, j=2.
		

Crossrefs

Cf. A204892, A205825.

Programs

Mathematica

s = Table[n!/Ceiling[n/2]!, {n, 1, 120}];
lk = Table[
  NestWhile[# + 1 &, 1,
   Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1,
    Length[s]}]
Table[NestWhile[# + 1 &, 1,
  Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]
(* Peter J. C. Moses, Jan 27 2012 *)