

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.


2



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
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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: A292376 A257685 A327172 * 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



