A205784 Least positive integer j such that n divides C(k)-C(j), where k, as in A205782, is the least number for which there is such a j, and C=A205824.

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

Offset

1,2

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..96.

Example

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

Mathematica

s = Table[(3 n)!/(3 n*n!*(n + 1)!), {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, A205824.

Sequence in context: A345058 A191654 A327983 * A066272 A237130 A330524

Adjacent sequences: A205781 A205782 A205783 * A205785 A205786 A205787

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved