A151774 Characteristic function of numbers with binary weight 2 (A018900).

0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane, Jun 23 2009

Keywords

• nonn
• easy

Comments

a(A018900(n)) = 1; a(A161989(n)) = 0. - Reinhard Zumkeller, Jun 24 2009

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for characteristic functions

Crossrefs

Cf. A000120, A018900, A151758.

Programs

Mathematica

w[n_] := IntegerDigits[n, 2] // Total;
a[n_] := Boole[w[n] == 2];
a /@ Range[0, 105] (* Jean-François Alcover, Mar 31 2021 *)

PARI

a(n)=hammingweight(n)==2 \\ Charles R Greathouse IV, Sep 26 2015

Formula

Let Theta = Sum_{k >= 0} x^(2^k). G.f. is (x + Theta^2 - Theta)/2 (cf. A151758).