A254377 Characteristic function of A230709: a(n) = 1 if n is either evil (A001969) or even odious (A128309), otherwise 0 (when n is odd odious).

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

Offset

0

Comments

A228495 is the characteristic function of the odd odious numbers (A092246).

A230709 is the union of even odious (A128309) and evil (A001969) numbers.

This sequence equals the parity of A003071, A093431, A122248, and A175186 (allowing for offsets).

Run lengths are given by A254378.

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.

Formula

a(n) = 1-A228495(n).

Mathematica

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

Prog

(PARI) A254377(n) = !((n%2)&&(hammingweight(n)%2)); \\ Antti Karttunen, Sep 27 2019
(Python)
def A254377(n): return n.bit_count()&1&n^1 # Chai Wah Wu, Mar 09 2023

Crossrefs

Cf. A000069, A001969, A010059, A010060, A092246, A128309, A228495, A230709, A254378.

Sequence in context: A267358 A368281 A153860 * A285657 A162519 A181359

Adjacent sequences: A254374 A254375 A254376 * A254378 A254379 A254380

Keyword

nonn,base

Author

Jeremy Gardiner, Jan 29 2015

Extensions

Secondary part of name added by Antti Karttunen, Sep 27 2019

Status

approved