TOPICS
Rabbit Sequence
Asequence which arises in the hypothetical reproduction of a population of rabbits. Let thesubstitution system map
correspond to young rabbits growing old, and
correspond to old rabbits producing young rabbits. Starting with 0 and iterating usingstring rewriting gives the terms 1, 10, 101, 10110, 10110101, 1011010110110, .... Arecurrence plot of the limiting value of this sequence is illustrated above.
Converted todecimal, this sequence gives 1, 2, 5, 22, 181, ... (OEISA005203), with the
th term given by therecurrence relation
 |
with
,
, and
the
thFibonacci number.
The limiting sequence written as abinaryfraction
(OEISA005614), where
denotes abinary number (i.e., a number written in base 2, so
or 1), is called therabbit constant.
See also
Fibonacci Number,RabbitConstant,Thue-Morse SequenceExplore with Wolfram|Alpha
References
Davison, J. L. "A Series and Its Associated Continued Fraction."Proc. Amer. Math. Soc.63, 29-32, 1977.Gould, H. W.; Kim, J. B.; and Hoggatt, V. E. Jr. "Sequences Associated witht-ary Coding of Fibonacci's Rabbits."Fib. Quart.15, 311-318, 1977.Schroeder, M.Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, p. 55, 1991.Sloane, N. J. A. SequencesA005203/M1539 andA005614 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Rabbit SequenceCite this as:
Weisstein, Eric W. "Rabbit Sequence."FromMathWorld--A Wolfram Web Resource.https://mathworld.wolfram.com/RabbitSequence.html