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%I #14 Feb 04 2022 09:22:59
%S 4,33,34,36,40,48,259,261,262,265,266,268,273,274,276,280,289,290,292,
%T 296,304,321,322,324,328,336,352,385,386,388,392,400,416,448,2055,
%U 2059,2061,2062,2067,2069,2070,2073,2074,2076,2083,2085,2086,2089,2090,2092
%N Numbers n such that (binary weight of n)/(length of binary representation of n) equals 1/3.
%C Generalization: numbers such that A000120(n)/A070939(n)=c. For c = 1 we have A000225, for c = 1/2 we have A031443. We may take c=p/q, 1 <= p < q. All sequences of this type show the same kind of "flocking" behavior.
%p q:= n-> (l-> nops(l)=3*add(i, i=l))(Bits[Split](n)):
%p select(q, [$1..2200])[]; # _Alois P. Heinz_, Feb 04 2022
%Y Cf. A000120, A070939, A000523, A000225, A031443.
%K base,easy,nonn
%O 1,1
%A _Ctibor O. Zizka_, Oct 15 2008