A173793 -id:A173793 - cp's OEIS frontend

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

T. D. Noe, Mar 03 2010

nonn

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.

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

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]]

A173800 Irregular triangle in which row n has primitive numbers k such that 1/k is in the Cantor set and the fraction 1/k has period n.

Original entry on oeis.org

1, 4, 13, 10, 40, 121, 28, 91, 364, 1093, 82, 328, 820, 3280, 757, 9841, 244, 7381, 29524, 88573, 730, 949, 2920, 6643, 9490, 20440, 26572, 66430, 265720, 797161, 2188, 597871, 2391484, 59293, 551881, 7174453, 6562, 26248, 65620, 253216

Offset: 1

T. D. Noe, Feb 25 2010

This sequence is a permutation of A173793. Row n ends with (3^n-1)/2. The length of row n is A173801(n).

T. D. Noe, Rows n=1..200, flattened

A173932 Least number m such that m/A173931(n) is a reduced fraction in the Cantor set.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 7, 1, 1, 1, 11, 17, 8, 1, 1, 1, 1, 1, 1, 37, 47, 19, 1, 1, 71, 25, 23, 1, 1, 1, 121, 43, 11, 5, 13, 2, 61, 59, 1, 1, 1, 197, 95, 28, 1, 1

Offset: 1

T. D. Noe, Mar 03 2010

nonn

When a(n)=1, then A173931(n) is in sequence A173793.

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

Cf. A173931, A173793, A173934.

First /@ Last[Transpose[cantor]] (* see A173931 *)

Name qualified by Peter Munn, Jul 12 2019

A175175 Number of primitive numbers k such that 1/k is in the Cantor set and 3^n <= k < 3^(n+1).

Original entry on oeis.org

1, 2, 2, 3, 3, 6, 5, 5, 6, 8, 7, 12, 7, 12, 11, 12, 8, 17, 10, 18, 19, 18, 14, 25, 18, 21, 23, 24, 19, 31, 21, 36, 28, 30, 25, 32, 27, 35, 24

Offset: 0

T. D. Noe, Feb 28 2010

nonn

Primitive means that 3 does not divide k. First differences of A173784. The values of k are in A173793.

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

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A173800 Irregular triangle in which row n has primitive numbers k such that 1/k is in the Cantor set and the fraction 1/k has period n.

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A173932 Least number m such that m/A173931(n) is a reduced fraction in the Cantor set.

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A175175 Number of primitive numbers k such that 1/k is in the Cantor set and 3^n <= k < 3^(n+1).

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