A205551 The least j such that n divides k^k-j^j, where k (as in A205546) is the least number for which there is such a j.

1, 1, 1, 2, 1, 2, 2, 4, 2, 4, 1, 2, 1, 2, 1, 4, 1, 2, 4, 4, 2, 1, 2, 4, 4, 1, 3, 2, 4, 4, 1, 4, 3, 4, 1, 2, 4, 1, 1, 4, 5, 2, 1, 1, 1, 2, 4, 4, 6, 4, 1, 1, 7, 3, 6, 6, 7, 4, 5, 4, 5, 2, 2, 4, 1, 3, 6, 4, 2, 6, 1, 8, 3, 1, 6, 1, 6, 3, 8, 4, 6, 5, 12, 2, 1, 4, 1, 6, 2, 6, 1, 2, 9, 4, 5, 4, 6, 6, 3

Offset: 1

Author

Clark Kimberling, Jan 31 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Examples

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

Crossrefs

Cf. A204892.

Programs

Mathematica

s = Table[n^n, {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 *)