A205787 Least positive integer k such that n divides k^3-j^3 for some j in [1,k-1].

2, 3, 4, 4, 6, 7, 2, 4, 4, 11, 12, 8, 3, 4, 16, 6, 18, 7, 3, 12, 4, 23, 24, 8, 10, 3, 6, 4, 30, 31, 5, 8, 34, 35, 9, 8, 4, 6, 5, 12, 42, 8, 6, 24, 16, 47, 48, 14, 5, 15, 52, 6, 54, 9, 56, 4, 7, 59, 60, 32, 5, 5, 4, 8, 14, 67, 7, 36, 70, 11, 72, 8, 8, 8, 20, 6, 15, 9, 7, 22, 12

Offset

1,1

Comments

For a guide to related sequences, see A204892.

1 divides 2^3-1^3 -> k=2, j=1

2 divides 3^3-1^3 -> k=3, j=1

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

4 divides 4^3-2^3 -> k=4, j=2

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

Links

Table of n, a(n) for n=1..81.

Mathematica

s = Table[n^3, {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

Sequence in context: A213635 A218443 A326035 * A072455 A177862 A066981

Adjacent sequences: A205784 A205785 A205786 * A205788 A205789 A205790

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved