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 A188068 [nr]-[kr]-[nr-kr], where r=sqrt(3), k=1, [ ]=floor. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS 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 See also A188014. REFERENCES J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A007538(n) - 2. [Reinhard Zumkeller, Feb 14 2012] MATHEMATICA 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*) PROG (Haskell) a188068 = (subtract 2) . a007538  -- Reinhard Zumkeller, Feb 14 2012 (Python) from gmpy2 import isqrt def A188068(n):     return int(isqrt(3*n**2) - isqrt(3*(n-1)**2)) - 1 # Chai Wah Wu, Oct 07 2016 CROSSREFS Cf. A188014. Sequence in context: A286746 A155897 A144610 * A181632 A105565 A332814 Adjacent sequences:  A188065 A188066 A188067 * A188069 A188070 A188071 KEYWORD nonn AUTHOR Clark Kimberling, Mar 20 2011 STATUS approved

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)