%I #24 Feb 07 2017 02:45:48

%S 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,

%T 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,

%U 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

%N [nr]-[kr]-[nr-kr], where r=sqrt(3), k=1, [ ]=floor.

%C 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

%C 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

%C See also A188014.

%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286.

%H Chai Wah Wu, <a href="/A188068/b188068.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007538(n) - 2. [_Reinhard Zumkeller_, Feb 14 2012]

%t r=3^(1/2)); k=1;

%t t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}] (*A188068*)

%t Flatten[Position[t,0]] (*A188069*)

%t Flatten[Position[t,1]] (*A188070*)

%o (Haskell)

%o a188068 = (subtract 2) . a007538 -- _Reinhard Zumkeller_, Feb 14 2012

%o (Python)

%o from gmpy2 import isqrt

%o def A188068(n):

%o return int(isqrt(3*n**2) - isqrt(3*(n-1)**2)) - 1 # _Chai Wah Wu_, Oct 07 2016

%Y Cf. A188014.

%K nonn

%O 1

%A _Clark Kimberling_, Mar 20 2011