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A205564 Least positive integer j such that n divides 2k!-2j!, where k, as in A205563, is the least number for which there is such a j. 0

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

%S 1,1,3,2,1,3,1,2,3,1,2,3,4,1,5,4,1,3,3,5,3,2,1,4,5,4,6,3,4,5,2,4,4,1,

%T 7,3,6,3,4,5,5,3,8,2,6,1,4,4,7,5,3,4,2,6,6,7,3,4,2,5,8,2,7,4,13,4,5,3,

%U 4,7,7,6,4,6,5,3,11,4,9,5,9,5,3,3,5,8,4,4,8,6,13,4,11,4,13,4

%N Least positive integer j such that n divides 2k!-2j!, where k, as in A205563, 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*4!-2*3! -> k=4, j=3

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

%e 5 divides 2*3!-2*1! -> k=3, j=1

%t s = Table[2n!, {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.

%K nonn

%O 1,3

%A _Clark Kimberling_, Feb 01 2012

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)