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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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For a guide to related sequences, see A204892. LINKS EXAMPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A204892. Sequence in context: A085068 A079587 A112745 * A036585 A164848 A213514 Adjacent sequences:  A205561 A205562 A205563 * A205565 A205566 A205567 KEYWORD nonn AUTHOR Clark Kimberling, Feb 01 2012 STATUS approved

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