A113503 - OEIS

%I #20 Nov 19 2017 04:44:14

%S 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,

%T 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,

%U 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

%N 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.

%H Michael De Vlieger, <a href="/A113503/b113503.txt">Table of n, a(n) for n = 1..16384</a> (First 210 terms from Diana L. Mecum).

%e 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).

%t 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 *)

%Y Cf. A113504, A000120.

%K base,nonn

%O 1,4

%A _Leroy Quet_, Jan 10 2006

%E More terms from _Diana L. Mecum_, May 29 2007