|
%I #10 Jul 10 2019 01:53:03
%S 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,
%T 9,10,12,13,27,28,30,31,36,37,39,40,5,11,15,33,45,47,5,15,41,45,47,59,
%U 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
%N 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.
%C 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.
%C 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.
%H T. D. Noe, <a href="/A173934/b173934.txt">Rows n=1..185, flattened</a>
%t Flatten[Last[Transpose[cantor]]] (* see A173931 *)
%Y Cf. A005836, A007734, A054591, A173931, A173933, A191106, A306556.
%K nonn,tabf
%O 1,3
%A _T. D. Noe_, Mar 03 2010
%E Name qualified by _Peter Munn_, Jul 06 2019
|
