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 A205563 Least positive integer k such that n divides 2k!-2j! for some j in [1,k-1]. 1

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

%S 2,2,4,3,3,4,5,3,4,3,4,4,9,5,6,5,5,4,5,6,6,4,4,5,6,9,7,6,6,6,10,5,7,5,

%T 8,4,13,5,9,6,7,6,11,4,7,4,10,5,8,6,6,9,12,7,8,8,5,6,5,6,16,10,8,5,14,

%U 7,8,6,8,8,9,7,8,13,6,5,12,9,14,6,10,7,19,6,11,11,6,7,10,7,14

%N Least positive integer k such that n divides 2k!-2j! for some j in [1,k-1].

%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 1,1

%A _Clark Kimberling_, Feb 01 2012

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Last modified June 22 21:17 EDT 2024. Contains 373609 sequences. (Running on oeis4.)