A205790 - OEIS

%I #7 Feb 28 2014 09:15:59

%S 1,1,1,1,1,2,3,1,4,1,5,2,2,6,1,1,1,3,9,1,2,10,11,2,3,1,3,6,2,2,15,3,4,

%T 3,3,3,1,18,1,1,4,4,21,10,3,22,23,2,7,1,1,1,2,3,4,6,8,3,29,2,5,30,1,2,

%U 2,8,33,3,10,6,35,3,3,5,1,18,2,1,39,1,3,1,41,4,1,42,2,10,5,3

%N Least positive integer j such that n divides k^4-j^4, where k, as in A205789, is the least number for which there is such a j.

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

%e 1 divides 2^4-1^4 -> k=2, j=1

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

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

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

%e 5 divides 2^4-1^4 -> k=2, j=1

%e 6 divides 4^4-2^4 -> k=4, j=2

%t s = Table[n^4, {n, 1, 120}] ;

%t lk = Table[

%t   NestWhile[# + 1 &, 1,

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

%t     Length[s]}]

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

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

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

%Y Cf. A204892.

%K nonn

%O 1,6

%A _Clark Kimberling_, Feb 01 2012