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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).
1
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved