%I A083567
%S A083567 21,37,42,45,53,69,73,74,81,83,84,90,106,133,137,138,141,146,148,155,
%T A083567 161,162,165,166,168,177,180,211,212,261,265,266,269,273,274,276,281,
%U A083567 282,289,291,292,295,296,299,310,321,322,324,330,332,336,354,359,360
%N A083567 Let B(n) be the number of binary digits in n. This is the sequence of 
               positive integers n such that 2B(n)=B(n^2).
%C A083567 This is the sequence of n such that the average of ones in binary expansion 
               of n is the same of the average of ones in binary expansion of n^2. 
               Conjecture.
%C A083567 The counting function p(n) p(n)=c n/log n + o(n/log n).
%D A083567 G. Melfi, On a family of positive integer sequences, in preparation.
%e A083567 a(1)=21 because 21=(10101) and 441=(110111001) and no smaller integer 
               has the property that 2B(n)=B(n^2).
%Y A083567 Cf. A077436.
%Y A083567 Sequence in context: A043751 A043759 A043768 this_sequence A109211 A050782 
               A061906
%Y A083567 Adjacent sequences: A083564 A083565 A083566 this_sequence A083568 A083569 
               A083570
%K A083567 easy,nonn
%O A083567 1,1
%A A083567 Giuseppe Melfi (Giuseppe.Melfi(AT)unine.ch), Jun 13 2003