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A189664 Fixed point of the morphism 0->010, 1->001. 8
0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

a(n) is the parity of the number of ternary 1-digits below the lowest 0-digit in the ternary expansion of n-1. All fixed-width morphisms have a similar digital interpretation. - Kevin Ryde, Apr 26 2017

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..2187

Index entries for sequences that are fixed points of mappings

FORMULA

a(3k-2)=0, a(3k-1)=1-a(k), a(3k)=a(k) for k>=1, a(0)=0.

2*a(n) = A284794(n) for n>=1. - Clark Kimberling, Apr 14 2017

a(n) = A284777(n) - 2n. - Clark Kimberling, Apr 15 2017

EXAMPLE

Iterating the morphism starting with 0:

0:   (#=1)

  0

1:   (#=3)

  010

2:   (#=9)

  010001010

3:   (#=27)

  010001010010010001010001010

4:   (#=81)

  010001010010010001010001010010001010010001010010010001010001010010010001010001010

etc.

MATHEMATICA

t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{0, 0, 1}}] &, {0}, 5] (*A189664*)

f[n_] := t[[n]]

Flatten[Position[t, 0]] (*A189665*)

Flatten[Position[t, 1]] (*A189666*)

s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;

Table[s[n], {n, 1, 120}] (*A189667*)

Nest[Flatten[# /. a_Integer -> {0, Abs[a - 1], a}] &, {0}, 5] (* Robert G. Wilson v, Jul 16 2012 *)

CROSSREFS

Cf. A189628, A189665, A189666, A189667.

Sequence in context: A134667 A117943 A285969 * A260446 A096268 A219097

Adjacent sequences:  A189661 A189662 A189663 * A189665 A189666 A189667

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 25 2011

STATUS

approved

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Last modified June 17 15:28 EDT 2019. Contains 324194 sequences. (Running on oeis4.)