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%I #33 Feb 05 2023 09:25:02
%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 Amiram Eldar, <a href="/A095111/b095111.txt">Table of n, a(n) for n = 0..10000</a>
%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) = A010059(A003714(n)).
%F a(n) = 1 - A095076(n).
%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
%t 1 - Mod[DigitCount[Select[Range[0, 540], BitAnd[#, 2 #] == 0 &], 2, 1], 2] (* _Amiram Eldar_, Feb 05 2023 *)
%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(1001) if ok(n)]) # _Indranil Ghosh_, Jun 08 2017
%Y Characteristic function of A095096.
%Y Run counts are given by A095276.
%Y Cf. A000045, A003714, A010059, A014417, A095076, A105774.
%K nonn
%O 0,1
%A _Antti Karttunen_, Jun 01 2004
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