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A205564
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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.
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0
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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, 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, 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
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OFFSET
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1,3
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COMMENTS
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For a guide to related sequences, see A204892.
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LINKS
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Table of n, a(n) for n=1..96.
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EXAMPLE
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1 divides 2*2!-2*1! -> k=2, j=1
2 divides 2*2!-2*1! -> k=2, j=1
3 divides 2*4!-2*3! -> k=4, j=3
4 divides 2*3!-2*2! -> k=3, j=2
5 divides 2*3!-2*1! -> k=3, j=1
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MATHEMATICA
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s = Table[2n!, {n, 1, 120}];
lk = Table[
NestWhile[# + 1 &, 1,
Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1,
Length[s]}]
Table[NestWhile[# + 1 &, 1,
Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]
(* Peter Moses, Jan 27 2012 *)
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CROSSREFS
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Cf. A204892.
Sequence in context: A085068 A079587 A112745 * A036585 A164848 A213514
Adjacent sequences: A205561 A205562 A205563 * A205565 A205566 A205567
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Feb 01 2012
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STATUS
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approved
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