Rabbit Constant
The limiting Rabbit Sequence written as a Binary Fraction 
(Sloane's A005614), where
denotes a Binary number (a number in base-2). The Decimal value is
(Sloane's A014565).
Amazingly, the rabbit constant is also given by the Continued Fraction [0, 
, 
, 
, 
,...], where 
are Fibonacci Numbers with 
taken as 0 (Gardner 1989, Schroeder 1991).Another amazing connection was discovered by S. Plouffe. Define the Beatty Sequence 
by
where
is the Floor Function and 
is the Golden Ratio. The first few terms are 1, 3, 4, 6,8, 9, 11, ... (Sloane's A000201). Then
See also Rabbit Sequence, Thue Constant, Thue-Morse Constant
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/cntfrc/cntfrc.html Gardner, M. Penrose Tiles and Trapdoor Ciphers... and the Return of Dr. Matrix, reissue ed. New York: W. H. Freeman, pp. 21-22, 1989. Plouffe, S. ``The Rabbit Constant to 330 Digits.''http://www.lacim.uqam.ca/piDATA/rabbit.txt. Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, p. 55, 1991. Sloane, N. J. A.A005614,A014565, andA000201/M2322in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Niven Number
- Niven's Constant
- n-minex
- Nobbs Points
- Noble Number
- Node (Algebraic Curve)
- Node (Fixed Point)
- Node (Graph)
- Noetherian Module
- Noetherian Ring
- Noether-Lasker Theorem
- Noether's Fundamental Theorem
- Noether's Transformation Theorem
- Noise
- Noise Sphere
- Nolid
- Nome
- n-Omino
- Nomogram
- Nonagon
- Nonagonal Number
- Nonagram
- Nonassociative Algebra
- Nonassociative Product
- Nonaveraging Sequence