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

Author

Clark Kimberling, Feb 01 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Examples

			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
		

Crossrefs

Cf. A204892, A007598.

Programs

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 *)