A205554 Least positive integer k such that n divides k^(k-1)-j^(j-1) for some j in [1,k-1].

2, 3, 4, 3, 4, 5, 3, 3, 4, 7, 4, 5, 5, 5, 7, 5, 5, 7, 7, 7, 4, 5, 6, 5, 6, 5, 7, 5, 12, 8, 4, 6, 5, 7, 11, 7, 9, 7, 5, 7, 8, 13, 7, 5, 7, 6, 12, 5, 8, 8, 5, 5, 7, 12, 4, 5, 7, 12, 12, 11, 12, 4, 4, 8, 7, 8, 7, 7, 7, 11, 7, 7, 9, 9, 8, 7, 5, 5, 8, 9, 9, 8, 10, 13, 7, 7, 14, 5, 5, 13, 16, 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, A205546, A000169.

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 *)