A205785 Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where C=A205825.

2, 3, 4, 5, 4, 5, 6, 5, 4, 4, 4, 6, 6, 8, 7, 7, 5, 5, 5, 6, 8, 7, 7, 8, 6, 7, 6, 9, 12, 7, 11, 9, 7, 10, 8, 6, 12, 7, 6, 8, 16, 8, 8, 9, 7, 12, 15, 9, 8, 6, 10, 7, 9, 6, 10, 9, 9, 12, 6, 8, 14, 11, 10, 9, 8, 7, 9, 10, 7, 8, 13, 10, 8, 12, 11, 14, 10, 8, 12, 10, 10, 16, 8, 9, 10, 14

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..86.

Example

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

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 *)

Crossrefs

Cf. A204892, A205825.

Sequence in context: A317646 A305748 A302981 * A303235 A350774 A282062

Adjacent sequences: A205782 A205783 A205784 * A205786 A205787 A205788

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved