The rabbit constant is the real number binary expansion rabbit
sequence as its binary digits (OEIS A005614 ).
Its decimal expansion begins
(1)
(OEIS A014565 ).
The rabbit constant is also given by the continued fraction [0; A000301 ), where Fibonacci
numbers with et al. 1995; Finch 2003, p. 439).
It also has a representation in terms of the Beatty
sequence
(2)
where positive integer , floor function ,
and golden ratio . The first few terms are 1, 3,
4, 6, 8, 9, 11, ... (OEIS A000201 ). Then
(3)
This representation is a special case of the Devil's staircase function with et al. 1995; Finch 2003, p. 439).
The irrationality measure of
See also Devil's Staircase ,
Rabbit Sequence ,
Thue Constant ,
Thue-Morse
Constant
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References Anderson, P. G.; Brown, T. C.; and Shiue, P. J.-S. "A Simple Proof of a Remarkable Continued Fraction Identity." Proc.
Amer. Math. Soc. 123 , 2005-2009, 1995. https://doi.org/10.1090/S0002-9939-1995-1249866-4 . Finch,
S. R. "Prouhet-Thue-Morse Constant." §6.8 in Mathematical
Constants. Gardner, M. Penrose
Tiles and Trapdoor Ciphers... and the Return of Dr. Matrix, reissue ed. Schroeder, M.
Fractals,
Chaos, Power Laws: Minutes from an Infinite Paradise. Sloane, N. J. A. Sequences A000201 /M2322,
A000301 , A005614 ,
and A014565 in "The On-Line Encyclopedia
of Integer Sequences." Referenced on Wolfram|Alpha Rabbit Constant
Cite this as:
Weisstein, Eric W. "Rabbit Constant."
From MathWorld https://mathworld.wolfram.com/RabbitConstant.html
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whose binary expansion 
has the rabbit
sequence as its binary digits (OEIS A005614).
Its decimal expansion begins
, 
, 
, 
, ...] = [0; 1, 2, 2, 4, 8, 32, 256, 8192, 2097152,
17179869184, ...] (OEIS A000301), where 
are Fibonacci
numbers with 
and 
(Gardner 1989, Schroeder 1991, Anderson et al. 1995; Finch 2003, p. 439).
It also has a representation in terms of the Beatty
sequence 
defined by
is a positive integer, 
is the floor function,
and 
is the golden ratio. The first few terms are 1, 3,
4, 6, 8, 9, 11, ... (OEIS A000201). Then
(Anderson et al. 1995; Finch 2003, p. 439).
is 
(D. Terr, pers. comm., May 21, 2004).
