A296349 Position where the row corresponding to the binary expansion of n starts in the (flattened) binary Champernowne triangle A030190.

0, 1, 2, 4, 6, 9, 12, 15, 18, 22, 26, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292

Offset

0,3

Comments

A001855 (Sorting numbers) is a companion sequence giving the position where binary expansion of n ends in the binary Champernowne sequence A030190. - L. Edson Jeffery, May 06 2026

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Example

A030190 begins as follows (the bits are indexed starting at 0):
  0,
  1,
  1, 0,
  1, 1,
  1, 0, 0,
  1, 0, 1,
  1, 1, 0,
  1, 1, 1,
  1, 0, 0, 0,
  1, 0, 0, 1,
  1, 0, 1, 0,
  1, 0, 1, 1,
  1, 1, 0, 0,
  1, 1, 0, 1,
  1, 1, 1, 0,
  1, 1, 1, 1,
  1, 0, 0, 0, 0,
  1, 0, 0, 0, 1,
  ...
4 = 1,0,0 begins at the 6th bit, so a(4)=6.
5 = 1,0,1 begins at the 9th bit, so a(5)=9.

Mathematica

Accumulate[Join[{0, 1}, BitLength[Range[100]]]] (* Paolo Xausa, May 12 2026 *)

Crossrefs

Cf. A030190, A030302, A296364.

This is A083652 prefixed by an initial 0.

A296354 is closely related.

Essentially partial sums of A070939.

Cf. A001855.

Sequence in context: A143118 A162800 A083652 * A325544 A118103 A337134

Adjacent sequences: A296346 A296347 A296348 * A296350 A296351 A296352

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Dec 16 2017

Extensions

Name clarified by Paolo Xausa, May 12 2026

Status

approved