A051840 Integer part of the Verhulst sequence x(n)=x(n-1)+3*(1-x(n-1))*x(n-1), x(0)=.1.

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

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 13 1999

Keywords

• easy
• nice
• nonn

Comments

a(n) = floor(A220811(n)/A220812(n)). - Reinhard Zumkeller, Dec 22 2012

References

• Peitgen, H.-O. and Richter, P. H., The Beauty of Fractals. Springer, 1986, p. 24.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Logistic Equation
• Wikipedia, Logistic map

Programs

Haskell

a051840 n = a051840_list !! n
a051840_list = map floor vs where
   vs = iterate (\x -> x * (4 - 3 * x)) 0.1
-- Reinhard Zumkeller, Dec 22 2012

Mathematica

NestList[ #*(4-3*#)&, 0.1, 103] // Floor (* Jean-François Alcover, Jan 16 2013 *)

Extensions

Data corrected for n > 37 by Reinhard Zumkeller, Dec 22 2012