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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.
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%I #6 Dec 04 2016 19:46:26

%S 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 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 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 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 For a guide to related sequences, see A204892.

%e 1 divides (2*2)!-(2*1)! -> k=2, j=1

%e 2 divides (2*2)!-(2*1)! -> k=2, j=1

%e 3 divides (2*3)!-(2*2)! -> k=3, j=2

%e 4 divides (2*3)!-(2*2)! -> k=3, j=2

%e 5 divides (2*4)!-(2*3)! -> k=4, j=3

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

%t lk = Table[NestWhile[# + 1 &, 1,

%t Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1, 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, A205551.

%K nonn

%O 1,3

%A _Clark Kimberling_, Feb 01 2012