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A205779
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Least positive integer j such that n divides C(k)-C(j), where k, as in A205778, is the least number for which there is such a j, and C=A000108 (Catalan numbers).
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0
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1, 1, 2, 1, 2, 2, 4, 2, 3, 2, 6, 2, 1, 4, 5, 4, 2, 5, 3, 2, 2, 6, 12, 4, 3, 2, 6, 4, 3, 5, 7, 2, 6, 2, 5, 2, 3, 10, 8, 2, 1, 2, 5, 8, 5, 12, 4, 4, 9, 9, 2, 8, 3, 2, 6, 5, 3, 2, 4, 2, 2, 2, 14, 8, 2, 8, 7, 2, 12, 5, 8, 12, 2, 10, 3, 10, 7, 8, 3, 8, 2, 2, 4, 2, 10, 6, 3, 8, 13, 5, 7, 12, 6
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OFFSET
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1,3
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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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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(3)-C(2) -> k=3, j=2
4 divides C(3)-C(1) -> k=3, j=1
5 divides C(5)-C(2) -> k=5, j=2
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MATHEMATICA
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s = Table[(2 n)!/(n!*(n + 1)!), {n, 1,
120}]; (* Catalan numbers *)
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]}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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