Happy easter sequence and constant.

[Simon Plouffe]

hello,

here is an interesting sequence (and constant).
....

%I A014565
%S A014565 0,7,0,9,8,0,3,4,4,2,8,6,1,2,9,1,3,1,4,6,4,1,7,8,7,3,9,9,4,4,4,5,7,5,5,9,7,0,1,2,5,
%T A014565 0,2,2,0,5,7,6,7,8,6,0,5,1,6,9,5,7,0,0,2,6,4,4,6,5,1,2,8,7,
%U A014565 1,2,8,1,4,8,4,6,5,9,6,2,4,7,8,3,1,6,1,3,2,4,5,9,9,9,3,8,8,3,9,2,6,5
%N A014565 Decimal digits of Rabbit Sequence.
%R A014565
%O A014565 0,2
%K A014565 nonn,more
%E A014565 How is this defined? (njas)
%D A014565 Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: W. H. Freeman,1991.
%H A014565 <a href="http://www.astro.virginia.edu/~eww6n/math/RabbitConstant.html">For further information</a>
%A A014565 Eric W. Weisstein (eww6n at carina.astro.virginia.edu), Simon Plouffe (plouffe at math.uqam.ca).


.709803442861291314641787399444575597012502205767860516957002644651287\
128148465962478316132459993883926539570334830469630528692315882422525170\
32515738024571669446181408309980068635294731038560074944148791425327670501\
6547500879857000915184454561847249659556239441319160312941620134935231843170\
421418998681668976495788059360606396788:


This is rabbit constant to 330 digits.

Define a(n) = floor(tau*n), tau = the Golden Ratio = 1/2 * (1+sqrt(5))

then define the number Sum(a(n)/2^n,n=1..infinity) = Rabbit Constant.

There is an interesting connection between that number and
sequences A014565, A005614 and the continued fraction
[0, 2^F(0), 2^F(1), 2^F(2), ...] where F(n) is the n'th Fibonacci number.

See also A000201 of the On-Line Encyclopedia of Integer Sequences
at
http://www.research.att.com/~njas/sequences/eisonline.html

and since this page was written near Easter 1998, here is a rabbit.

               (`.         ,-,
               `\ `.    ,;' /
                \`. \ ,'/ .'
          __     `.\ Y /.'
       .-'  ''--.._` ` (
     .'            /   `
    ,           ` '   oo'
    ,         ,   `._    \
    |         '     `-.;_'
    `  ;    `  ` --,.._;
    `    ,   )   .'
     `._ ,  '   /_
        ; ,''-,;' ``-
         ``-..__\``--`

see also http://www.lacim.uqam.ca/piDATA/rabbit.txt


Simon Plouffe