A380911 Triangle read by rows: Row n is the initial segment [1, 2, ..., n] sorted into lexicographic order defined by the binary representation of the terms.

1, 1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 5, 3, 6, 1, 2, 4, 5, 3, 6, 7, 1, 2, 4, 8, 5, 3, 6, 7, 1, 2, 4, 8, 9, 5, 3, 6, 7, 1, 2, 4, 8, 9, 5, 10, 3, 6, 7, 1, 2, 4, 8, 9, 5, 10, 11, 3, 6, 7, 1, 2, 4, 8, 9, 5, 10, 11, 3, 6, 12, 7

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of triangle, flattened).

Example

Triangle starts:
  [1]  [1]
  [2]  [1, 2]
  [3]  [1, 2, 3]
  [4]  [1, 2, 4, 3]
  [5]  [1, 2, 4, 5, 3]
  [6]  [1, 2, 4, 5, 3, 6]
  [7]  [1, 2, 4, 5, 3, 6, 7]
  [8]  [1, 2, 4, 8, 5, 3, 6, 7]
  [9]  [1, 2, 4, 8, 9, 5, 3, 6, 7]
  [10] [1, 2, 4, 8, 9, 5, 10, 3, 6, 7]
.
The binary representations of the numbers 1..12 in lexicographic order are:
[1, 10, 100, 1000, 1001, 101, 1010, 1011, 11, 110, 1100, 111]. Therefore row 12 is
[1, 2, 4, 8, 9, 5, 10, 11, 3, 6, 12, 7].

Maple

row := proc(n) sort(convert~([$n], binary), key=String); (convert~(%, decimal, 2)) end:
seq(op(row(n)), n = 1..12);

Mathematica

A380911row[n_] := Map[FromDigits[#, 2] &, Sort[IntegerString[Range[n], 2]]];
Array[A380911row, 15] (* Paolo Xausa, Feb 08 2025 *)

Crossrefs

Cf. A007088.

Sequence in context: A265692 A370263 A376308 * A194976 A195082 A210535

Adjacent sequences: A380907 A380909 A380910 * A380912 A380913 A380914

Keyword

nonn,tabl,base,new

Author

Peter Luschny, Feb 08 2025

Status

approved