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

5, 11, 17, 20, 23, 29, 35, 41, 44, 47, 53, 59, 65, 68, 71, 77, 80, 83, 89, 92, 95, 101, 107, 113, 116, 119, 125, 131, 137, 140, 143, 149, 155, 161, 164, 167, 173, 176, 179, 185, 188, 191, 197, 203, 209, 212, 215, 221, 227, 233, 236, 239, 245

Offset: 1

Author

Ralf Stephan, May 11 2003

Keywords

• nonn
• easy

Comments

Numbers that are both in A016789 and A003159.

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]

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for 2-automatic sequences.

Crossrefs

Intersection of A016789 and A003159.

Cf. A084091.

A352273 without the multiples of 9.

Programs

Mathematica

Select[3 * Range[0, 81] + 2, EvenQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 16 2022 *)

PARI

for(n=0,300,if(valuation(n,2)%2==0&&n%3==2,print1(n",")))

Python

from itertools import count, islice
def A084088_gen(): # generator of terms
    return filter(lambda n:(n&-n).bit_length()&1,count(2,3))
A084088_list = list(islice(A084088_gen(),30)) # Chai Wah Wu, Jul 11 2022