A173934 Irregular triangle in which row n consists of numbers m < k/2 such that m/k is in the Cantor set, where k= A173931(n) and gcd(m,k) = 1.

1, 1, 3, 1, 3, 4, 1, 3, 9, 1, 3, 9, 13, 1, 3, 7, 9, 19, 21, 25, 27, 1, 3, 9, 10, 27, 30, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 5, 11, 15, 33, 45, 47, 5, 15, 41, 45, 47, 59, 7, 16, 21, 22, 48, 61, 63, 66, 1, 3, 7, 9, 19, 21, 25, 27, 55, 57, 63, 73, 75, 79, 81, 1, 3, 9, 27

Offset

1,3

Comments

The length of row n is A173933(n). Observe that the m are actually less than k/3. Note that (k-m)/k is also in the Cantor set. If m appears in a row, then 3m does also. Let A and B be the first and last numbers in row n, then it appears that k = A + 3B. This implies A = k (mod 3). The interesting graph of this triangle shows that some ranges of m are not allowed.

When k is a prime of the form (3^r-1)/2, then the row consists of the 2^(r-1)-1 numbers (greater than 0) whose base-3 representation consists of only 0's and 1's. Hence, for r=3,7, and 13, the primes k are 13, 1093, and 797161, and the number of m < k/2 is 3, 63, and 4095.

Links

T. D. Noe, Rows n=1..185, flattened

Mathematica

Flatten[Last[Transpose[cantor]]] (* see A173931 *)

Crossrefs

Cf. A005836, A007734, A054591, A173931, A173933, A191106, A306556.

Sequence in context: A329512 A064884 A093560 * A131504 A008311 A175721

Adjacent sequences: A173931 A173932 A173933 * A173935 A173936 A173937

Keyword

nonn,tabf

Author

T. D. Noe, Mar 03 2010

Extensions

Name qualified by Peter Munn, Jul 06 2019

Status

approved