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%I #6 Dec 04 2016 19:46:26
%S 2,3,2,4,3,3,4,5,2,3,5,5,6,4,3,6,7,3,8,4,5,5,9,6,4,6,3,4,11,3,3,7,5,7,
%T 4,5,7,8,6,6,12,5,6,5,3,9,9,6,6,4,7,6,7,3,6,5,8,11,18,6,7,10,5,7,7,5,
%U 9,7,9,4,18,6,17,7,8,8,5,6,18,7,10,12,12,5,7,6,11,6,13,3,6,9,3
%N Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where 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 1,1
%A _Clark Kimberling_, Feb 01 2012