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

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, 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, 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

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..91.

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 J. C. Moses, Jan 27 2012 *)

Crossrefs

Cf. A204892.

Sequence in context: A162439 A154417 A292421 * A147594 A305425 A212652

Adjacent sequences: A205560 A205561 A205562 * A205564 A205565 A205566

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved