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A188068
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[nr]-[kr]-[nr-kr], where r=sqrt(3), k=1, [ ]=floor.
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10
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0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1
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OFFSET
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1
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COMMENTS
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Sturmian word with slope alpha = sqrt(3)-1, and offset 0. Since alpha has a periodic continued fraction expansion with period 12, (a(n+1)) is the unique fixed point of the morphism 0 -> 110, 1 -> 1101. - Michel Dekking, Feb 06 2017
A275855(n) = R(a(n)) for n>1, where R is the mirror morphism R(0)=1, R(1)=0, This can be shown by induction on the iterates of the two morphisms generating the sequences. - Michel Dekking, Feb 07 2017
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286.
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LINKS
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FORMULA
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MATHEMATICA
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r=3^(1/2)); k=1;
t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r], {n, 1, 220}] (*A188068*)
Flatten[Position[t, 0]] (*A188069*)
Flatten[Position[t, 1]] (*A188070*)
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PROG
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(Haskell)
(Python)
from gmpy2 import isqrt
return int(isqrt(3*n**2) - isqrt(3*(n-1)**2)) - 1 # Chai Wah Wu, Oct 07 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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