The On-Line Encyclopedia of Integer Sequences (OEIS)

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A283963

Fixed point of the morphism 0 -> 1, 1 -> 1010.
(history; published version)

#9 by N. J. A. Sloane at Thu Apr 27 11:34:52 EDT 2017

STATUS

proposed

approved

#8 by Clark Kimberling at Thu Apr 27 09:34:09 EDT 2017

STATUS

editing

proposed

#7 by Clark Kimberling at Thu Apr 27 09:25:57 EDT 2017

LINKS

<a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

STATUS

approved

editing

#6 by N. J. A. Sloane at Sun Mar 26 11:51:02 EDT 2017

STATUS

proposed

approved

#5 by Jon E. Schoenfield at Sat Mar 25 16:03:18 EDT 2017

STATUS

editing

proposed

#4 by Jon E. Schoenfield at Sat Mar 25 16:03:14 EDT 2017

NAME

Fixed point of the morphism 0 -> 1, 1 -> 1010.

COMMENTS

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

EXAMPLE

1 -> 1010 -> 1010110101 -> 1010110101101010101101011010 ->

STATUS

proposed

editing

#3 by Clark Kimberling at Sat Mar 25 11:39:06 EDT 2017

STATUS

editing

proposed

#2 by Clark Kimberling at Sat Mar 25 11:34:57 EDT 2017

NAME

allocated for Clark KimberlingFixed point of the morphism 0->1, 1->1010.

DATA

1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1

OFFSET

1

COMMENTS

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

LINKS

Clark Kimberling, <a href="/A283963/b283963.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

1->1010->1010110101->1010110101101010101101011010->

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0}}] &, {0}, 10] (* A283963 *)

Flatten[Position[s, 0]] (* A283964 *)

Flatten[Position[s, 1]] (* A283965 *)

CROSSREFS

Cf. A283964, A283965.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Mar 25 2017

STATUS

approved

editing

#1 by Clark Kimberling at Sat Mar 18 12:52:15 EDT 2017

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved