A173931 Primitive numbers k such that m/k is in the Cantor set for some m.

4, 10, 13, 28, 40, 82, 91, 121, 146, 182, 205, 244, 328, 364, 386, 656, 671, 730, 757, 820, 949, 1036, 1093, 1342, 1640, 2044, 2188, 2362, 2555, 2644, 2684, 2812, 2920, 3280, 3640, 3796, 3851, 4088, 4561, 4745, 5110, 6176, 6562, 6643, 7381, 7592, 7913

Offset: 1

Author

T. D. Noe, Mar 03 2010

Keywords

• nonn

Comments

Primitive means no k is a multiple of 3. This is sequence A054591 without the multiples of 3. Sequence A173793 is a subsequence. Sequence A173932 gives the least m such for each k. Sequence A173933 gives the number of m < k/2 such that m/k is in the Cantor set. Irregular triangle A173934 gives a row of m values for each k.

The remaining terms <10000 are 9139, 9490, 9841.

It is assumed that gcd(m,k) = 1.

Links

• T. D. Noe, Table of n, a(n) for n=1..185

Programs

Mathematica

InCantorQ[m_, n_] := !MemberQ[Union[Flatten[RealDigits[m/n,3][[1]]]], 1]; cantor=Reap[Do[If[Mod[n,3] > 0, s=Select[Range[Ceiling[n/2]], GCD[n,# ]==1 && InCantorQ[ #,n] &]; If[s != {}, Sow[{n, s}]]], {n,10000}]][[2,1]]; First[Transpose[cantor]]