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A205780
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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).
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1
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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
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OFFSET
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1,1
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COMMENTS
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For a guide to related sequences, see A204892.
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LINKS
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Table of n, a(n) for n=1..89.
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EXAMPLE
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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
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MATHEMATICA
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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 Moses, Jan 27 2012 *)
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CROSSREFS
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Cf. A204892, A007598.
Sequence in context: A026256 A079715 A030397 * A204905 A082597 A112212
Adjacent sequences: A205777 A205778 A205779 * A205781 A205782 A205783
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Feb 01 2012
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STATUS
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approved
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