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 A205784 Least positive integer j such that n divides C(k)-C(j), where k, as in A205782, is the least number for which there is such a j, and C=A205824. 0

%I

%S 1,2,1,3,2,2,3,3,1,2,4,4,5,3,2,5,6,2,7,3,4,4,8,5,2,5,2,3,10,2,1,6,4,6,

%T 3,4,2,7,5,3,11,4,3,4,2,8,8,5,3,2,6,5,6,2,4,3,7,10,7,4,2,6,4,6,6,4,2,

%U 6,8,3,9,5,8,2,7,7,4,5,2,6,7,11,10,4,6,3,10,5,9,2,5,8,1,8,7,6

%N Least positive integer j such that n divides C(k)-C(j), where k, as in A205782, is the least number for which there is such a j, and C=A205824.

%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(2) -> k=3, j=2

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

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

%e 5 divides C(3)-C(2) -> k=3, j=2

%t s = Table[(3 n)!/(3 n*n!*(n + 1)!), {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, A205824.

%K nonn

%O 1,2

%A _Clark Kimberling_, Feb 01 2012

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)