A091855 Odious numbers (see A000069) in A003159.

1, 4, 7, 11, 13, 16, 19, 21, 25, 28, 31, 35, 37, 41, 44, 47, 49, 52, 55, 59, 61, 64, 67, 69, 73, 76, 79, 81, 84, 87, 91, 93, 97, 100, 103, 107, 109, 112, 115, 117, 121, 124, 127, 131, 133, 137, 140, 143, 145, 148, 151, 155, 157, 161, 164, 167, 171, 173, 176, 179, 181

Offset: 1

Author

Philippe Deléham, Mar 16 2004

Keywords

• easy
• nonn

Comments

Also n such that A033485(n) == 1 (mod 4); see A007413.

Also n such that A029883(n-1) = 1, A036577(n-1) = 2, A036585(n-1) = 3. - Philippe Deléham, Mar 25 2004

The number of odd numbers before the n-th even number in this sequence is a(n). - Philippe Deléham, Mar 27 2004

Numbers n such that {A010060(n-1), A010060(n)}={0,1} where A010060 is the Thue-Morse sequence. - Benoit Cloitre, Jun 16 2006

Positive integers not of the form n+A010060(n). - Jeffrey Shallit, Feb 13 2024

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 42-46.
• Index entries for 2-automatic sequences.

Programs

Mathematica

A036554 := Select[Range[70500], OddQ[IntegerExponent[#, 2]] &]; Table[ A036554[[2*n - 1]]/2, {n, 1, 100}] (* G. C. Greubel, Jan 14 2018 *)

PARI

is(n)=hammingweight(n)%2 && valuation(n,2)%2==0 \\ Charles R Greathouse IV, May 09 2016

Formula

a(n) = A003159(2n-1) = A036554(2n-1)/2.

a(n) is asymptotic to 3*n - Benoit Cloitre, Mar 22 2004

A050292(a(n)) = 2n - 1. - Philippe Deléham, Mar 26 2004

Extensions

More terms from Benoit Cloitre, Mar 22 2004