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A095076 Parity of 1-fibits in Zeckendorf expansion A014417(n). 7
0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 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, 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, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let u=A000201=(lower Wythoff sequence) and v=A001950=(upper Wythoff sequence.  Conjecture: This sequence is the sequence p given by p(1)=0 and p(u(k))=p(k); p(v(k))=1-p(k). [Clark Kimberling, Apr 15 2011]

[base 2] 0.111010010001100... = 0.9105334708635617... [Joerg Arndt, May 13 2011]

REFERENCES

Leonard Rozendaal, [https://hal.archives-ouvertes.fr/hal-01552281 Pisano word, tesselation, plane-filling fractal], Preprint, 2017.

LINKS

Table of n, a(n) for n=0..101.

Joerg Arndt, Matters Computational (The Fxtbook), section 38.11.1, pp. 754-756

E. Ferrand, An analogue of the Thue-Morse sequence, The Electronic Journal of Combinatorics, Volume 14 (2007), R30.

Index entries for characteristic functions

MATHEMATICA

r=(1+5^(1/2))/2; u[n_] := Floor[n*r];  (*A000201*)

a[1] = 0; h = 128;

c = (u[#1] &) /@ Range[2h];

d = (Complement[Range[Max[#1]], #1] &)[c]; (*A001950*)

Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];

Table[a[c[[n]]] = a[n], {n, 1, h}] (*A095076 conjectured*)

Flatten[Position[%, 0]]  (*A189034*)

Flatten[Position[%%, 1]] (*A189035*)

PROG

(Python)

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

print [bin(n)[2:].count("1")%2 for n in xrange(0, 1001) if ok(n)] # Indranil Ghosh, Jun 08 2017

CROSSREFS

a(n) = A010060(A003714(n)). a(n) = 1 - A095111(n). Characteristic function of A020899. Run counts are given by A095276.

Cf. A189034, A189035 (positions of 0 and 1 if the conjecture is valid.

Sequence in context: A174206 A265333 A159637 * A285080 A167392 A190201

Adjacent sequences:  A095073 A095074 A095075 * A095077 A095078 A095079

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 01 2004

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)