A091855 - OEIS

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

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OFFSET

1,2

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.

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

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A345347 A310720 A310721 * A191404 A288374 A308199

Adjacent sequences: A091852 A091853 A091854 * A091856 A091857 A091858

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Mar 16 2004

EXTENSIONS

More terms from Benoit Cloitre, Mar 22 2004

STATUS

approved