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

0,6

Links

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

Example

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;
  ...

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)<b(y) or b(x)=b(y) and x<y)[]:
seq(T(n), n=0..6);  # Alois P. Heinz, Mar 31 2025

Mathematica

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

Crossrefs

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

Main diagonal gives A000225.

Last elements of rows give A131577.

Row sums give A006516.

Sequence in context: A286223 A341163 A329278 * A348966 A008783 A139144

Adjacent sequences: A382464 A382465 A382466 * A382468 A382469 A382470

Keyword

nonn,tabf,look,base,easy

Author

Paolo Xausa, Mar 31 2025

Status

approved