A102392 Odious numbers in odious places.

0, 1, 2, 0, 4, 0, 0, 7, 8, 0, 0, 11, 0, 13, 14, 0, 16, 0, 0, 19, 0, 21, 22, 0, 0, 25, 26, 0, 28, 0, 0, 31, 32, 0, 0, 35, 0, 37, 38, 0, 0, 41, 42, 0, 44, 0, 0, 47, 0, 49, 50, 0, 52, 0, 0, 55, 56, 0, 0, 59, 0, 61, 62, 0, 64, 0, 0, 67, 0, 69, 70, 0, 0, 73, 74, 0, 76, 0, 0, 79, 0, 81, 82, 0, 84, 0

Offset: 0

Author

Paul Barry, Jan 06 2005

Keywords

• easy
• nonn
• base

Comments

Odious numbers A000069(n) appear at positions indexed by the odious numbers, 0 otherwise.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000069, A000120, A001477, A010060, A102391, A102392.

Programs

Mathematica

odnQ[n_]:=OddQ[DigitCount[n,2,1]]; Table[If[odnQ[n],n,0],{n,0,100}] (* Harvey P. Dale, Oct 15 2019 *)

Python

def A102392(n): return n*(n.bit_count()&1) # Chai Wah Wu, Nov 23 2023

Formula

A001477(n) = A102391(n)+a(n).

a(n) = if((1+floor(n/2))(1+(-1)^A000120(n))/2=0, n, 0).

a(n) = if((1+floor(n/2))(1+(-1)^A010060(n))/2=0, n, 0).

a(n) = n*A010060(n). - Ridouane Oudra, Apr 19 2025