A205780 Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where C=A007598 (squared Fibonacci numbers).

2, 3, 2, 3, 3, 4, 4, 3, 5, 5, 5, 4, 5, 6, 5, 4, 7, 6, 7, 5, 4, 7, 7, 4, 9, 7, 7, 6, 7, 5, 8, 6, 6, 7, 6, 6, 8, 9, 5, 6, 10, 6, 10, 7, 10, 10, 8, 6, 11, 9, 9, 7, 9, 7, 5, 6, 9, 9, 12, 5, 13, 13, 5, 8, 8, 10, 19, 7, 12, 13, 11, 6, 11, 19, 9, 9, 8, 8, 23, 6, 10, 12, 22, 6, 10, 10, 8, 7, 9

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..89.

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: A030397 A379604 A257213 * A204905 A082597 A112212

Adjacent sequences: A205777 A205778 A205779 * A205781 A205782 A205783

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved