A205781 Least positive integer j such that n divides C(k)-C(j), where k, as in A205780, is the least number for which there is such a j, and C=A007598 (squared Fibonacci numbers).

1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 4, 1, 2, 3, 6, 4, 2, 2, 2, 1, 2, 1, 4, 4, 3, 1, 5, 2, 3, 3, 2, 6, 5, 4, 3, 7, 4, 3, 8, 1, 3, 1, 1, 3, 6, 4, 3, 4, 6, 4, 2, 3, 3, 1, 2, 3, 3, 2, 12, 4, 1, 2, 7, 1, 2, 6, 10, 6, 2, 4, 2, 16, 4, 7, 1, 5, 4, 3, 5, 6, 11, 1, 7, 3, 4, 1, 8, 1, 5, 3, 4, 4, 3, 2, 5

Offset

1,5

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..97.

Example

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

Mathematica

s = Table[(Fibonacci[n + 1])^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, A007598.

Sequence in context: A266476 A081327 A363279 * A357982 A280444 A030422

Adjacent sequences: A205778 A205779 A205780 * A205782 A205783 A205784

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved