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
Keywords
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=4, j=2
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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 *)
Comments