A205790 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.

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, 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, 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

Offset

1,6

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..90.

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: A218534 A241773 A348388 * A279820 A235791 A035426

Adjacent sequences: A205787 A205788 A205789 * A205791 A205792 A205793

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved