A205794 Least positive integer j such that n divides C(k)-C(j) , where k, as in A205793, is the least number for which there is such a j, and C=A002808 (composite numbers).

1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2

Offset

1,3

Comments

Is this sequence bounded? For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..99.

Example

1 divides C(2)-C(1) -> k=2, j=1
2 divides C(2)-C(1) -> k=2, j=1
3 divides C(4)-C(2) -> k=4, j=2
4 divides C(3)-C(1) -> k=3, j=1
5 divides C(4)-C(1) -> k=4, j=1
6 divides C(5)-C(1) -> k=5, j=1

Mathematica

s = Select[Range[2, 120], ! PrimeQ[#] &]
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: A111604 A101491 A276949 * A241665 A175307 A324825

Adjacent sequences: A205791 A205792 A205793 * A205795 A205796 A205797

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved