A084090 - OEIS

%I #13 Jan 16 2022 08:19:17

%S 0,2,3,6,8,9,10,12,14,15,18,21,22,24,26,27,30,32,33,34,36,38,39,40,42,

%T 45,46,48,50,51,54,56,57,58,60,62,63,66,69,70,72,74,75,78,81,82,84,86,

%U 87,88,90,93,94,96,98,99,102,104,105,106,108,110,111

%N Numbers k such that k is divisible by 3 or the exponent of the highest power of 2 dividing k is odd. Complement of A084087.

%C Numbers that are either in A008585 or A036554.

%C It seems that lim_{n->inf} a(n)/n = 9/5. [This is true. The asymptotic density of this sequence is 5/9. - _Amiram Eldar_, Jan 16 2022]

%C Positions of 0 in the expansion of Sum_{k>=0} x^2^k/(1+x^2^k+x^2^(k+1)) (A084091).

%H Amiram Eldar, <a href="/A084090/b084090.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[0,120],Divisible[#,3]||OddQ[IntegerExponent[#,2]]&] (* _Harvey P. Dale_, Jul 26 2017 *)

%o (PARI) for(n=0,300,if(valuation(n,2)%2||n%3==0,print1(n",")))

%Y Union of A008585 and A036554.

%Y Cf. A084087, A084091.

%K nonn

%O 1,2

%A _Ralf Stephan_, May 11 2003