A113503 a(1) = 1. For n >= 2, a(n) is the number of earlier terms of the sequence that have the same number of ones in their binary representations as n.

1, 1, 0, 2, 0, 0, 0, 3, 1, 1, 0, 1, 0, 0, 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 10, 3, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 4, 4, 1, 4, 1, 1, 0, 4, 1, 1, 0, 1, 0, 0, 0, 4, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 1, 1, 0

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..16384 (First 210 terms from Diana L. Mecum).

Example

The first 7 terms written in binary are [1,1,0,10,0,0,0]. The 8th term gives the number of earlier terms with the same number of 1's in their binary representation as 8 (which is 1000 in binary, for one 1). a(8) = 3 because there are three terms among the first 7 terms with one binary 1 (terms with one 1: 1, 1 and 2).

Mathematica

Fold[Append[#1, Block[{b = DigitCount[#2, 2, 1]}, {#, DigitCount[#, 2, 1]} &@ Count[#1[[All, -1]], k_ /; k == b]]] &, {{1, 1}}, Range[2, 99]][[All, 1]] (* Michael De Vlieger, Nov 18 2017 *)

Crossrefs

Cf. A113504, A000120.

Sequence in context: A347233 A327172 A355524 * A082507 A132349 A216226

Adjacent sequences: A113500 A113501 A113502 * A113504 A113505 A113506

Keyword

base,nonn

Author

Leroy Quet, Jan 10 2006

Extensions

More terms from Diana L. Mecum, May 29 2007

Status

approved