A205554 - OEIS

%I #7 Dec 04 2016 19:46:26

%S 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,

%T 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,

%U 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

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

%C For a guide to related sequences, see A204892.

%e 1 divides 2^(2-1)-1^(1-1) -> k=2, j=1

%e 2 divides 3^(3-1)-1^(1-1) -> k=3, j=1

%e 3 divides 4^(4-1)-1^(1-1) -> k=4, j=1

%e 4 divides 3^(3-1)-1^(1-1) -> k=3, j=1

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

%t s = Table[n^(n-1), {n, 1, 120}];

%t lk = Table[NestWhile[# + 1 &, 1,

%t    Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1, Length[s]}]

%t Table[NestWhile[# + 1 &, 1,

%t   Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &],

%t {j, 1, Length[lk]}]

%t (* _Peter J. C. Moses_, Jan 27 2012 *)

%Y Cf. A204892, A205546, A000169.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 01 2012