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

1, 4, 7, 13, 16, 19, 25, 28, 31, 37, 43, 49, 52, 55, 61, 64, 67, 73, 76, 79, 85, 91, 97, 100, 103, 109, 112, 115, 121, 124, 127, 133, 139, 145, 148, 151, 157, 163, 169, 172, 175, 181, 187, 193, 196, 199, 205, 208, 211, 217, 220, 223, 229, 235

Offset: 1

Author

Ralf Stephan, May 11 2003

Keywords

• nonn
• easy

Comments

Numbers that are both in A016777 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 A003159 and A016777.

Cf. A084091.

A352274 without the multiples of 3.

Programs

Mathematica

Select[3 * Range[0, 81] + 1, EvenQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 16 2022 *)

PARI

for(n=0,300,if(valuation(n,2)%2==0&&n%3==1,print1(n",")))

Python

from itertools import count, islice
def A084089_gen(): # generator of terms
    return filter(lambda n:(n&-n).bit_length()&1,count(1,3))
A084089_list = list(islice(A084089_gen(),30)) # Chai Wah Wu, Jul 11 2022