A254379 Characteristic function of the even odious numbers (A128309).

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, 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, 0, 0, 1, 0, 1

Offset

0

Comments

a(n) is also the characteristic function of A129771 (the odd evil numbers), offset by 1.

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

The characteristic function of the odious numbers (A000069) is given by the Thue-Morse sequence (A010060).

Links

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

Index entries for characteristic functions.

Formula

a(n) = A059841(n)*A010060(n) = 1-A254651(n). - Antti Karttunen, Oct 01 2018

Example

A128309 begins 2, 4, 8, hence this sequence begins 0, 0, 1, 0, 1, 0, 0, 0, 1.

Mathematica

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

Prog

(PARI) a(n)=n%2==0 && hammingweight(n)%2 \\ Charles R Greathouse IV, May 09 2016
(Python)
def A254379(n): return (n&1^1)&n.bit_count() # Chai Wah Wu, Mar 09 2023

Crossrefs

Cf. A000069, A010060, A059841, A092246, A128309, A129771, A228495, A254651, A254655 (run lengths).

Sequence in context: A353463 A260445 A156731 * A288257 A285666 A120325

Adjacent sequences: A254376 A254377 A254378 * A254380 A254381 A254382

Keyword

nonn,easy,base

Author

Jeremy Gardiner, Jan 29 2015

Status

approved