A030301 n-th run has length 2^(n-1).

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

Offset: 1

Author

Jean-Paul Delahaye

Keywords

• nonn
• base
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for characteristic functions

Crossrefs

Cf. A000523, A029837.

Cf. A030300. Partial sums give A079954.

Characteristic function of A053754 (after its initial 0).

Programs

Magma

[Floor(Log(n)/Log(2)) mod 2: n in [1..100]]; // Vincenzo Librandi, Jun 23 2015

Mathematica

nMax = 7; Table[1 - Mod[n, 2], {n, nMax}, {2^(n-1)}] // Flatten (* Jean-François Alcover, Oct 20 2016 *)
Table[{PadRight[{},2^(n-1),0],PadRight[{},2^n,1]},{n,1,8,2}]//Flatten (* Harvey P. Dale, Apr 12 2023 *)

PARI

a(n)=if(n<1,0,1-length(binary(n))%2)

PARI

a(n)=if(n<1,0,if(n%2==0,-a(n/2)+1,-a((n-1)/2)+1-(((n-1)/2)==0))) /* Ralf Stephan */

Python

def A030301(n): return n.bit_length()&1^1 # Chai Wah Wu, Jan 30 2023

Formula

a(n) = A000523(n) mod 2 = (A029837(n+1)+1) mod 2.

a(n) = 0 iff n has an odd number of digits in binary, = 1 otherwise. - Henry Bottomley, Apr 06 2000

a(n) = (1/2)*{1-(-1)^floor(log(n)/log(2))}. - Benoit Cloitre, Nov 22 2001

a(n) = 1-a(floor(n/2)). - Vladeta Jovovic, Aug 04 2003

a(n) = 1 - A030300(n). - Antti Karttunen, Oct 10 2017