A205779 - OEIS

%I #6 Dec 04 2016 19:46:26

%S 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,

%T 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,

%U 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

%N 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).

%C For a guide to related sequences, see A204892.

%e 1 divides C(2)-C(1) -> k=2, j=1

%e 2 divides C(3)-C(1) -> k=3, j=1

%e 3 divides C(3)-C(2) -> k=3, j=2

%e 4 divides C(3)-C(1) -> k=3, j=1

%e 5 divides C(5)-C(2) -> k=5, j=2

%t s = Table[(2 n)!/(n!*(n + 1)!), {n, 1,

%t    120}]; (* Catalan numbers *)

%t lk = Table[

%t   NestWhile[# + 1 &, 1,

%t    Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1,

%t     Length[s]}]

%t Table[NestWhile[# + 1 &, 1,

%t   Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]

%t (* _Peter J. C. Moses_, Jan 27 2012 *)

%Y Cf. A204892, A000108.

%K nonn

%O 1,3

%A _Clark Kimberling_, Feb 01 2012