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A283966 Fixed point of the morphism 0 -> 1, 1 -> 10101. 3
1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0 (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 = (7+sqrt(17))/4 and s = (-1+sqrt(17))/2, so that 1/r + 1/s = 1. Conjecture: -1 <  n*r - u(n) < 3 and -1 < n*s - v(n) < 2 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 -> 10101 -> 10101110101110101 -> ...

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0, 1}}] &, {0}, 10] (* A283966 *)

Flatten[Position[s, 0]]  (* A283967 *)

Flatten[Position[s, 1]]  (* A284015 *)

CROSSREFS

Cf. A283967, A284015.

Sequence in context: A245837 A245656 A285625 * A054354 A156728 A267442

Adjacent sequences:  A283963 A283964 A283965 * A283967 A283968 A283969

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 26 2017

STATUS

approved

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Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)