A205789 Least positive integer k such that n divides k^4-j^4 for some j in [1,k-1].

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, 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, 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

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..87.

Example

1 divides 2^4-1^4 -> k=2, j=1
2 divides 3^4-1^4 -> k=3, j=1
3 divides 2^4-1^4 -> k=2, j=1
4 divides 3^4-1^4 -> k=3, j=1
5 divides 2^4-1^4 -> k=2, j=1
6 divides 4^4-2^4 -> k=4, j=2

Mathematica

s = Table[n^4, {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.

Sequence in context: A278354 A165005 A167530 * A029208 A322592 A329896

Adjacent sequences: A205786 A205787 A205788 * A205790 A205791 A205792

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved