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A284386 Fixed point of the morphism 0->1, 1->1101. 1
1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Let u(n) = # 0's <= n and v(n) = # 1's <= n.  Let r = (5+sqrt(3))/2 and s = (-1+sqrt(13))/2, so that 1/r + 1/s = 1.  Conjecture:  0 <  n*r - u(n) < 2 and -1 < n*s - v(n) < 1 for n >= 1.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

Index entries for sequences that are fixed points of mappings

EXAMPLE

1->1101-> 1101110111101->

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 1, 0, 1}}] &, {0}, 13]; (* A284386 *)

Flatten[Position[s, 0]];  (* A184483 *)

Flatten[Position[s, 1]];  (* A184482 *)

CROSSREFS

Cf. A184483, A184482.

Sequence in context: A229343 A188082 A285599 * A286922 A285668 A267813

Adjacent sequences:  A284383 A284384 A284385 * A284387 A284388 A284389

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 26 2017

STATUS

approved

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Last modified October 18 10:28 EDT 2017. Contains 293507 sequences.