A205786 - OEIS

%I #9 Apr 12 2016 06:46:08

%S 1,1,3,4,2,2,1,4,3,2,1,4,3,7,6,2,3,2,1,5,7,4,3,6,5,2,4,8,5,6,4,8,4,8,

%T 7,4,5,5,3,6,12,7,3,6,6,6,3,8,7,5,8,2,3,4,7,8,3,5,2,6,6,4,9,8,6,4,7,8,

%U 3,7,6,9,1,5,10,9,7,6,8,8,9,12,5,8,8,9,6,6,1,6,7,6,4,11,5,8,8

%N Least positive integer j such that n divides C(k)-C(j), where k, as in A205785, is the least number for which there is such a j, and C=A205825.

%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(4)-C(3) -> k=4, j=3;

%e 4 divides C(5)-C(4) -> k=5, j=4;

%e 5 divides C(4)-C(2) -> k=4, j=2.

%t s = Table[n!/Ceiling[n/2]!, {n, 1, 120}];

%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, A205825.

%K nonn

%O 1,3

%A _Clark Kimberling_, Feb 01 2012