A132680 Number of ones in binary representation of odious numbers.

1, 1, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 5, 1, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 5, 5, 5, 1, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 5, 5, 5, 3, 3, 3, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 7, 1, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 5, 3, 5, 5, 5, 3, 3, 3, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 5, 5, 7, 3, 3, 3, 5, 3, 5, 5, 5, 3

Offset: 1

Author

Reinhard Zumkeller, Aug 26 2007

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10001
• Eric Weisstein's World of Mathematics, Odious Number.
• Eric Weisstein's World of Mathematics, Thue-Morse Sequence.
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000069, A000120, A010060, A005408, A083420, A129771.

Programs

Mathematica

Select[DigitCount[Range[200], 2, 1], OddQ] (* Amiram Eldar, Jul 22 2023 *)

PARI

a(n)=hammingweight(2*n-1-hammingweight(n-1)%2) \\ Charles R Greathouse IV, Mar 26 2013

Formula

a(n) = a(floor(n/2)) + 2*(n mod 2)*(1-A010060(n)).

a(n) = A000120(A000069(n)).

a(A129771(n)) = a((A129771(n)-1)/2) + 2.

a(A083420(n)) = A005408(n).