A205793 Least positive integer k such that n divides C(k)-C(j) for some j in [1,k-1], where C=A002808 (composite numbers).

2, 2, 4, 3, 4, 5, 8, 6, 8, 7, 8, 9, 12, 10, 12, 11, 12, 13, 15, 14, 15, 16, 17, 18, 21, 19, 21, 20, 21, 22, 23, 24, 26, 25, 26, 27, 30, 28, 30, 29, 30, 31, 33, 32, 33, 34, 35, 36, 38, 37, 38, 39, 40, 41, 44, 42, 44, 43, 44, 45, 46, 47, 49, 48, 49, 50, 53, 51, 53, 52

Offset

1,1

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..70.

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: A177235 A079707 A233511 * A178431 A233574 A353925

Adjacent sequences: A205790 A205791 A205792 * A205794 A205795 A205796

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved