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

1,1

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

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

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 *)

Prog

(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 */
(Magma) [Floor(Log(n)/Log(2)) mod 2: n in [1..100]]; // Vincenzo Librandi, Jun 23 2015
(Python)
def A030301(n): return n.bit_length()&1^1 # Chai Wah Wu, Jan 30 2023

Crossrefs

Cf. A000523, A029837.

Cf. A030300. Partial sums give A079954.

Characteristic function of A053754 (after its initial 0).

Sequence in context: A284789 A288736 A270803 * A316341 A284901 A071981

Adjacent sequences: A030298 A030299 A030300 * A030302 A030303 A030304

Keyword

nonn,base,easy

Author

Jean-Paul Delahaye

Status

approved