A228495 Characteristic function of the odd odious numbers (A092246).

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

Offset

0,1

Comments

The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008.

a(n+1) is the characteristic function of the even evil numbers (A125592). - Jeremy Gardiner, Feb 06 2015

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Tanya Khovanova, There are no coincidences, arXiv preprint 1410.2193 [math.CO], 2014.

Index entries for characteristic functions.

Index entries for sequences related to binary expansion of n.

Formula

a(2n) = 0, a(2n+1) = A092436(n).

a(n) = A000035(n) * A010060(n). - Antti Karttunen, Jan 12 2019

Mathematica

a[n_] := If[OddQ[n] && OddQ[DigitCount[n, 2, 1]], 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Aug 06 2023 *)

Prog

(PARI) a(n)=if(n%2==0, 0, subst(Pol(binary((n-1)/2)), x, 1)%2==0)
(PARI) A228495(n) = ((n%2)&&(hammingweight(n)%2)); \\ Antti Karttunen, Jan 12 2019
(Python)
def A228495(n): return n.bit_count()&1&n # Chai Wah Wu, Mar 03 2023

Crossrefs

Cf. A000035, A010060, A092246, A092436, A125592, A254379.

Cf. A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975.

Sequence in context: A300477 A355202 A353556 * A356982 A284683 A369968

Adjacent sequences: A228492 A228493 A228494 * A228496 A228497 A228498

Keyword

nonn,base

Author

Ralf Stephan, Aug 23 2013

Status

approved