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A095111 One minus the parity of 1-fibits in Zeckendorf expansion A014417(n). 4


%S 1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,

%T 0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,

%U 1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1

%N One minus the parity of 1-fibits in Zeckendorf expansion A014417(n).

%D Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

%H Leonard Rozendaal, <a href="https://hal.archives-ouvertes.fr/hal-01552281">Pisano word, tesselation, plane-filling fractal</a>, Preprint, 2017.

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

%F a(n)=a'(n+1) where a'(1)=1 and if n>=2 with F(k)<n<=F(k+1) a'(n)=1-a'(n-F(k)) where F(k)=A000045(k). E, g. F(5)=5<6<=F(6)=8 thus a'(6)=1-a'(1)=0 and a(5)=0. - _Benoit Cloitre_, May 10 2005

%o (Python)

%o def ok(n): return 1 if n==0 else n*(2*n & n == 0)

%o print [1 - bin(n)[2:].count("1")%2 for n in range(0, 1001) if ok(n)] # _Indranil Ghosh_, Jun 08 2017

%Y a(n) = A010059(A003714(n)). a(n) = 1 - A095076(n). Characteristic function of A095096. Run counts are given by A095276.

%Y Cf. A105774.

%K nonn

%O 0,1

%A _Antti Karttunen_, Jun 01 2004

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)