A038870 Irregular triangle read by rows: T(n,k) = number of orbits of order exactly k under doubling map which remain in a semicircle, with k dividing n.

0, 1, 1, 3, 1, 7, 1, 5, 11, 15, 1, 31, 1, 9, 21, 43, 55, 63, 1, 37, 91, 127, 1, 17, 85, 171, 239, 255, 1, 73, 439, 511, 1, 33, 137, 293, 341, 683, 731, 887, 991, 1023, 1, 661, 1387, 2047, 1, 65, 273, 585, 1189, 1365, 2731, 2907, 3511, 3823, 4031, 4095, 1

Offset

1,4

Comments

If alpha = exp(2*i*Pi*T(n,k)/(2^n - 1)), the orbit of alpha has period n and stays in the semicircle of minimal argument alpha.

Links

Table of n, a(n) for n=1..59.

Formula

T(n, k) = Sum_{j=0..n-1} 2^[n*j/k], for k such that (k, n)=1.

Example

Triangle begins:
  0;
  1;
  1, 3;
  1, 7;
  1, 5, 11, 15;
  1, 31;
  1, 9, 21, 43, 55, 63;
  1, 37, 91, 127;
  1, 17, 85, 171, 239, 255;
  1, 73, 439, 511;
  1, 33, 137, 293, 341, 683, 731, 887, 991, 1023;
  ...
with the length of each row given by phi(n) = A000010(n).

Crossrefs

Cf. A038871.

Sequence in context: A227873 A117677 A324377 * A347234 A324865 A316553

Adjacent sequences: A038867 A038868 A038869 * A038871 A038872 A038873

Keyword

nonn,tabf,easy

Author

Francois Maurel (maurel(AT)sequoia.ens.fr)

Extensions

Revised by Sean A. Irvine, Feb 16 2021

Status

approved