A205546 Least positive integer k such that n divides k^k-j^j for some j in [1,k-1].

2, 3, 2, 4, 4, 4, 4, 6, 4, 6, 5, 4, 3, 4, 4, 6, 4, 4, 5, 6, 4, 5, 3, 8, 6, 3, 6, 4, 6, 8, 6, 6, 6, 8, 6, 4, 7, 9, 8, 6, 9, 4, 6, 5, 8, 8, 10, 8, 8, 6, 4, 9, 9, 9, 8, 8, 8, 6, 9, 8, 10, 12, 4, 6, 8, 9, 9, 8, 8, 8, 5, 10, 10, 9, 12, 9, 8, 9, 9, 6, 9, 9, 18, 4, 4, 16, 7, 8, 8, 12, 8, 8, 12, 10

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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=4, j=2

Maple

f:= proc(n) local S, k, v;
  S:= {}:
  for k from 1 do
    v:= k &^ k mod n;
    if member(v, S) then return k fi;
    S:= S union {v}
  od
end proc:
map(f, [$1..100]); # Robert Israel, Aug 23 2023

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 *)

Crossrefs

Cf. A204892, A000312.

Sequence in context: A235805 A168231 A235728 * A322348 A081315 A035662

Adjacent sequences: A205543 A205544 A205545 * A205547 A205548 A205549

Keyword

nonn

Author

Clark Kimberling, Jan 31 2012

Status

approved