A205555 Least positive integer j such that n divides k^(k-1)-j^(j-1), where k (as in A205554) is the least positive integer for which there is such a j.

1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 1, 3, 4, 1, 4, 1, 1, 3, 1, 3, 2, 1, 1, 1, 4, 3, 8, 2, 2, 4, 4, 3, 9, 1, 5, 1, 1, 3, 2, 1, 1, 3, 4, 2, 2, 1, 1, 2, 4, 1, 5, 6, 3, 3, 1, 8, 7, 1, 5, 2, 1, 4, 4, 2, 4, 3, 5, 9, 2, 1, 8, 5, 2, 1, 3, 1, 7, 1, 6, 2, 4, 1, 3, 1, 2, 3, 2, 1, 1, 5, 2, 2, 5, 5, 4, 1, 7

Offset: 1

Author

Clark Kimberling, Feb 01 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Examples

			1 divides 2^(2-1)-1^(1-1) -> k=2, j=1
2 divides 3^(3-1)-1^(1-1) -> k=3, j=1
3 divides 4^(4-1)-1^(1-1) -> k=4, j=1
4 divides 3^(3-1)-1^(1-1) -> k=3, j=1
5 divides 4^(4-1)-3^(3-1) -> k=4, j=3
		

Crossrefs

Cf. A204892, A205551.

Programs

Mathematica

s = Table[n^(n-1), {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 *)