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Least positive integer k such that n divides k^4-j^4 for some j in [1,k-1].
1

%I #6 Dec 04 2016 19:46:26

%S 2,3,2,3,2,4,4,3,5,3,6,4,3,8,2,3,4,9,10,3,5,12,12,4,4,5,6,8,5,4,16,5,

%T 7,5,4,9,6,20,5,3,5,10,22,12,6,24,24,4,14,7,4,5,7,9,7,8,11,7,30,4,6,

%U 32,8,6,3,14,34,5,13,8,36,9,8,7,7,20,9,5,40,3,6,9,42,10,4,44,5

%N Least positive integer k such that n divides k^4-j^4 for some j in [1,k-1].

%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 1,1

%A _Clark Kimberling_, Feb 01 2012