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A205562
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.
0
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, 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, 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
OFFSET
1,3
COMMENTS
For a guide to related sequences, see A204892.
EXAMPLE
1 divides (2*2)!-(2*1)! -> k=2, j=1
2 divides (2*2)!-(2*1)! -> k=2, j=1
3 divides (2*3)!-(2*2)! -> k=3, j=2
4 divides (2*3)!-(2*2)! -> k=3, j=2
5 divides (2*4)!-(2*3)! -> k=4, j=3
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 J. C. Moses, Jan 27 2012 *)
CROSSREFS
Sequence in context: A141829 A111336 A083902 * A217984 A196437 A106491
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved