A205778 - OEIS

%I #7 Dec 04 2016 19:46:26

%S 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,

%T 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,

%U 15,19,6,9,11,8,13,12,21,13,17,12,8,12,8,9,12,16,9,17,7,8,11,9

%N Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where 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 1,1

%A _Clark Kimberling_, Feb 01 2012