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

1,4

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.

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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A268498 A059787 A081325 * A105595 A072219 A173854

Adjacent sequences: A132677 A132678 A132679 * A132681 A132682 A132683

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 26 2007

Status

approved