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A205562 Least positive integer j such that n divides (2k)!-(2j)!, where k, as in A205561, is the least number for which there is such a j.

%I A205562 #6 Dec 04 2016 19:46:26
%S A205562 1,1,2,2,3,2,4,2,3,3,1,2,7,4,3,3,9,3,1,3,4,1,2,2,3,7,5,4,2,3,1,4,3,9,
%T A205562 4,3,19,1,7,3,4,4,1,3,3,2,2,3,4,3,9,7,1,5,3,4,5,2,12,3,4,1,4,4,7,3,1,
%U A205562 9,2,4,2,3,2,19,3,5,6,7,2,3,5,4,12,4,9,1,2,3,4,3,7,2,6,2,5,4,1
%N A205562 Least positive integer j such that n divides (2k)!-(2j)!, where k, as in A205561, is the least number for which there is such a j.
%C A205562 For a guide to related sequences, see A204892.
%e A205562 1 divides (2*2)!-(2*1)! -> k=2, j=1
%e A205562 2 divides (2*2)!-(2*1)! -> k=2, j=1
%e A205562 3 divides (2*3)!-(2*2)! -> k=3, j=2
%e A205562 4 divides (2*3)!-(2*2)! -> k=3, j=2
%e A205562 5 divides (2*4)!-(2*3)! -> k=4, j=3
%t A205562 s = Table[(2n)!, {n, 1, 120}];
%t A205562 lk = Table[NestWhile[# + 1 &, 1,
%t A205562    Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1, Length[s]}]
%t A205562 Table[NestWhile[# + 1 &, 1,
%t A205562   Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]
%t A205562 (* _Peter J. C. Moses_, Jan 27 2012 *)
%Y A205562 Cf. A204892, A205551.
%K A205562 nonn
%O A205562 1,3
%A A205562 _Clark Kimberling_, Feb 01 2012