A382467 Irregular triangle read by rows, where row n lists the integers from 0 to 2^n - 1 sorted by the number of zeros in their binary representation (in case of ties, by their decimal value).

0, 0, 1, 0, 1, 3, 2, 0, 1, 3, 7, 2, 5, 6, 4, 0, 1, 3, 7, 15, 2, 5, 6, 11, 13, 14, 4, 9, 10, 12, 8, 0, 1, 3, 7, 15, 31, 2, 5, 6, 11, 13, 14, 23, 27, 29, 30, 4, 9, 10, 12, 19, 21, 22, 25, 26, 28, 8, 17, 18, 20, 24, 16, 0, 1, 3, 7, 15, 31, 63, 2, 5, 6, 11, 13, 14, 23, 27, 29, 30

Offset: 0

Author

Paolo Xausa, Mar 31 2025

Keywords

• nonn
• tabf
• look
• base
• easy

Examples

			Triangle begins:
  [0]  0;
  [1]  0,  1;
  [2]  0,  1,  3,  2;
  [3]  0,  1,  3,  7,  2,  5,  6,  4;
  [4]  0,  1,  3,  7, 15,  2,  5,  6, 11, 13, 14,  4,  9, 10, 12,  8;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..8190 (rows 0..12 of triangle, flattened).

Crossrefs

Cf. A080791, A294648 (sorted by number of ones).

Main diagonal gives A000225.

Last elements of rows give A131577.

Row sums give A006516.

Programs

Maple

b:= proc(n) b(n):= add(1-i, i=Bits[Split](n)) end:
T:= n-> sort([$0..2^n-1], (x, y)-> b(x)Alois P. Heinz, Mar 31 2025

Mathematica

Table[SortBy[Range[0, 2^n - 1], DigitCount[#, 2, 0] &], {n, 0, 6}]