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%I #7 Feb 28 2014 09:15:09
%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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