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A205779
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).
0
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
OFFSET
1,3
COMMENTS
For a guide to related sequences, see A204892.
EXAMPLE
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
MATHEMATICA
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]}]
(* Peter J. C. Moses, Jan 27 2012 *)
CROSSREFS
Sequence in context: A161833 A294100 A139318 * A205551 A281130 A054541
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved