A205779 Least positive integer j such that n divides C(k)-C(j), where k, as in A205778, is the least number for which there is such a j, and C=A000108 (Catalan numbers).

1, 1, 2, 1, 2, 2, 4, 2, 3, 2, 6, 2, 1, 4, 5, 4, 2, 5, 3, 2, 2, 6, 12, 4, 3, 2, 6, 4, 3, 5, 7, 2, 6, 2, 5, 2, 3, 10, 8, 2, 1, 2, 5, 8, 5, 12, 4, 4, 9, 9, 2, 8, 3, 2, 6, 5, 3, 2, 4, 2, 2, 2, 14, 8, 2, 8, 7, 2, 12, 5, 8, 12, 2, 10, 3, 10, 7, 8, 3, 8, 2, 2, 4, 2, 10, 6, 3, 8, 13, 5, 7, 12, 6

Offset

1,3

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..93.

Example

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

Mathematica

s = Table[(2 n)!/(n!*(n + 1)!), {n, 1,
   120}]; (* Catalan numbers *)
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, A000108.

Sequence in context: A161833 A294100 A139318 * A205551 A281130 A054541

Adjacent sequences: A205776 A205777 A205778 * A205780 A205781 A205782

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved