A084087 Numbers k not divisible by 3 such that the exponent of the highest power of 2 dividing k is even.

1, 4, 5, 7, 11, 13, 16, 17, 19, 20, 23, 25, 28, 29, 31, 35, 37, 41, 43, 44, 47, 49, 52, 53, 55, 59, 61, 64, 65, 67, 68, 71, 73, 76, 77, 79, 80, 83, 85, 89, 91, 92, 95, 97, 100, 101, 103, 107, 109, 112, 113, 115, 116, 119, 121, 124, 125, 127, 131

Offset: 1

Author

Ralf Stephan, May 11 2003

Keywords

• nonn
• easy

Comments

Numbers that are in both A001651 and A003159.

Numbers that are in either A084088 or A084089.

Complement of union of ({k==0 (mod 3)}, {2a(n)}) (A084090).

It seems that lim_{n->infinity} a(n)/n = 9/4. [This is true. The asymptotic density of this sequence is 4/9. - Amiram Eldar, Jan 16 2022]

Positions of nonzero coefficients 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 (terms 1..1000 from Harvey P. Dale)
• Index entries for 2-automatic sequences.

Crossrefs

Disjoint union of A084089 and A084090.

Intersection of A001651 and A003159.

Also subsequence of A036668, A339690.

Cf. A084088, A084091.

Programs

Mathematica

Select[Range[200],Mod[#,3]!=0&&EvenQ[IntegerExponent[#,2]]&] (* Harvey P. Dale, May 15 2018 *)

PARI

for(n=0,100,if(valuation(n,2)%2==0&&n%3,print1(n",")))