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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.)