cp's OEIS Frontend

A084089 Numbers k such that k == 1 (mod 3) and the exponent of the highest power of 2 dividing k is even.

%I A084089 #25 Jul 11 2022 11:15:33
%S A084089 1,4,7,13,16,19,25,28,31,37,43,49,52,55,61,64,67,73,76,79,85,91,97,
%T A084089 100,103,109,112,115,121,124,127,133,139,145,148,151,157,163,169,172,
%U A084089 175,181,187,193,196,199,205,208,211,217,220,223,229,235
%N A084089 Numbers k such that k == 1 (mod 3) and the exponent of the highest power of 2 dividing k is even.
%C A084089 Numbers that are both in A016777 and A003159.
%C A084089 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 A084089 Positions of +1 in the expansion of Sum_{k>=0} x^2^k/(1+x^2^k+x^2^(k+1)) (A084091).
%H A084089 Amiram Eldar, <a href="/A084089/b084089.txt">Table of n, a(n) for n = 1..10000</a>
%H A084089 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%t A084089 Select[3 * Range[0, 81] + 1, EvenQ[IntegerExponent[#, 2]] &] (* _Amiram Eldar_, Jan 16 2022 *)
%o A084089 (PARI) for(n=0,300,if(valuation(n,2)%2==0&&n%3==1,print1(n",")))
%o A084089 (Python)
%o A084089 from itertools import count, islice
%o A084089 def A084089_gen(): # generator of terms
%o A084089     return filter(lambda n:(n&-n).bit_length()&1,count(1,3))
%o A084089 A084089_list = list(islice(A084089_gen(),30)) # _Chai Wah Wu_, Jul 11 2022
%Y A084089 Intersection of A003159 and A016777.
%Y A084089 Cf. A084091.
%Y A084089 A352274 without the multiples of 3.
%K A084089 nonn,easy
%O A084089 1,2
%A A084089 _Ralf Stephan_, May 11 2003