cp's OEIS Frontend

A084088 Numbers k such that k == 2 (mod 3) and the exponent of the highest power of 2 dividing k is even.

%I A084088 #21 Jul 11 2022 11:15:29
%S A084088 5,11,17,20,23,29,35,41,44,47,53,59,65,68,71,77,80,83,89,92,95,101,
%T A084088 107,113,116,119,125,131,137,140,143,149,155,161,164,167,173,176,179,
%U A084088 185,188,191,197,203,209,212,215,221,227,233,236,239,245
%N A084088 Numbers k such that k == 2 (mod 3) and the exponent of the highest power of 2 dividing k is even.
%C A084088 Numbers that are both in A016789 and A003159.
%C A084088 It seems that lim_{n->oo} a(n)/n = 9/2. [This is true. The asymptotic density of this sequence is 2/9. - _Amiram Eldar_, Jan 16 2022]
%C A084088 Positions of -1 in the expansion of Sum_{k>=0} x^2^k/(1+x^2^k+x^2^(k+1)) (A084091).
%H A084088 Amiram Eldar, <a href="/A084088/b084088.txt">Table of n, a(n) for n = 1..10000</a>
%H A084088 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%t A084088 Select[3 * Range[0, 81] + 2, EvenQ[IntegerExponent[#, 2]] &] (* _Amiram Eldar_, Jan 16 2022 *)
%o A084088 (PARI) for(n=0,300,if(valuation(n,2)%2==0&&n%3==2,print1(n",")))
%o A084088 (Python)
%o A084088 from itertools import count, islice
%o A084088 def A084088_gen(): # generator of terms
%o A084088     return filter(lambda n:(n&-n).bit_length()&1,count(2,3))
%o A084088 A084088_list = list(islice(A084088_gen(),30)) # _Chai Wah Wu_, Jul 11 2022
%Y A084088 Intersection of A016789 and A003159.
%Y A084088 Cf. A084091.
%Y A084088 A352273 without the multiples of 9.
%K A084088 nonn,easy
%O A084088 1,1
%A A084088 _Ralf Stephan_, May 11 2003