A030301 - OEIS

%I #38 Apr 12 2023 10:07:52

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A030301/b030301.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%F a(n) = 0 iff n has an odd number of digits in binary, = 1 otherwise. - _Henry Bottomley_, Apr 06 2000

%F a(n) = (1/2)*{1-(-1)^floor(log(n)/log(2))}. - _Benoit Cloitre_, Nov 22 2001

%F a(n) = 1-a(floor(n/2)). - _Vladeta Jovovic_, Aug 04 2003

%F a(n) = 1 - A030300(n). - _Antti Karttunen_, Oct 10 2017

%t nMax = 7; Table[1 - Mod[n, 2], {n, nMax}, {2^(n-1)}] // Flatten (* _Jean-François Alcover_, Oct 20 2016 *)

%t Table[{PadRight[{},2^(n-1),0],PadRight[{},2^n,1]},{n,1,8,2}]//Flatten (* _Harvey P. Dale_, Apr 12 2023 *)

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

%o (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_ */

%o (Magma) [Floor(Log(n)/Log(2)) mod 2: n in [1..100]]; // _Vincenzo Librandi_, Jun 23 2015

%o (Python)

%o def A030301(n): return n.bit_length()&1^1 # _Chai Wah Wu_, Jan 30 2023

%Y Cf. A000523, A029837.

%Y Cf. A030300. Partial sums give A079954.

%Y Characteristic function of A053754 (after its initial 0).

%K nonn,base,easy

%O 1,1

%A _Jean-Paul Delahaye_