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A205778
Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where C=A000108 (Catalan numbers).
1
2, 3, 3, 3, 5, 4, 5, 5, 4, 5, 7, 4, 4, 5, 6, 9, 8, 6, 8, 5, 8, 8, 13, 8, 8, 6, 7, 5, 10, 6, 9, 11, 7, 8, 12, 9, 5, 11, 9, 5, 5, 8, 7, 9, 6, 13, 15, 9, 13, 12, 8, 9, 7, 9, 9, 11, 8, 14, 6, 9, 7, 12, 15, 19, 6, 9, 11, 8, 13, 12, 21, 13, 17, 12, 8, 12, 8, 9, 12, 16, 9, 17, 7, 8, 11, 9
OFFSET
1,1
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: A092308 A205394 A213617 * A328972 A081831 A349837
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved