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%I #29 Jan 16 2022 09:18:23
%S 1,4,5,7,11,13,16,17,19,20,23,25,28,29,31,35,37,41,43,44,47,49,52,53,
%T 55,59,61,64,65,67,68,71,73,76,77,79,80,83,85,89,91,92,95,97,100,101,
%U 103,107,109,112,113,115,116,119,121,124,125,127,131
%N Numbers k not divisible by 3 such that the exponent of the highest power of 2 dividing k is even.
%C Numbers that are in both A001651 and A003159.
%C Numbers that are in either A084088 or A084089.
%C Complement of union of ({k==0 (mod 3)}, {2a(n)}) (A084090).
%C It seems that lim_{n->infinity} a(n)/n = 9/4. [This is true. The asymptotic density of this sequence is 4/9. - _Amiram Eldar_, Jan 16 2022]
%C Positions of nonzero coefficients in the expansion of Sum_{k>=0} x^2^k/(1 + x^2^k + x^2^(k+1)) (A084091).
%H Amiram Eldar, <a href="/A084087/b084087.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%t Select[Range[200],Mod[#,3]!=0&&EvenQ[IntegerExponent[#,2]]&] (* _Harvey P. Dale_, May 15 2018 *)
%o (PARI) for(n=0,100,if(valuation(n,2)%2==0&&n%3,print1(n",")))
%Y Disjoint union of A084089 and A084090.
%Y Intersection of A001651 and A003159.
%Y Also subsequence of A036668, A339690.
%Y Cf. A084088, A084091.
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, May 11 2003
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