A205778 Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where C=A000108 (Catalan numbers).

2, 3, 3, 3, 5, 4, 5, 5, 4, 5, 7, 4, 4, 5, 6, 9, 8, 6, 8, 5, 8, 8, 13, 8, 8, 6, 7, 5, 10, 6, 9, 11, 7, 8, 12, 9, 5, 11, 9, 5, 5, 8, 7, 9, 6, 13, 15, 9, 13, 12, 8, 9, 7, 9, 9, 11, 8, 14, 6, 9, 7, 12, 15, 19, 6, 9, 11, 8, 13, 12, 21, 13, 17, 12, 8, 12, 8, 9, 12, 16, 9, 17, 7, 8, 11, 9

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(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: A092308 A205394 A213617 * A328972 A081831 A349837

Adjacent sequences: A205775 A205776 A205777 * A205779 A205780 A205781

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved