A220811 -id:A220811 - cp's OEIS frontend

A220812 Denominators of the Verhulst sequence x(n+1)=4x(n)-3x(n)^2, x(0)=1/10.

10, 100, 10000, 100000000, 10000000000000000, 100000000000000000000000000000000, 10000000000000000000000000000000000000000000000000000000000000000

Offset: 0

Reinhard Zumkeller, Dec 22 2012

H. O. Peitgen and P. H. Richter, The Beauty of Fractals. Springer, 1986, p. 23f.

Reinhard Zumkeller, Table of n, a(n) for n = 0..9
Eric Weisstein's World of Mathematics, Logistic Equation
Wikipedia, Logistic map

Cf. A051840, A220811 (numerators).

a220812 = a011557 . a000079  -- Reinhard Zumkeller, Dec 22 2012

a(n) = 10^(2^n) = A011557(A000079(n)). - Reinhard Zumkeller, Dec 22 2012

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

Original entry on oeis.org

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

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

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

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

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

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

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

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

cp's OEIS Frontend

A220812 Denominators of the Verhulst sequence x(n+1)=4x(n)-3x(n)^2, x(0)=1/10.

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

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cp's OEIS Frontend

A220812 Denominators of the Verhulst sequence x(n+1)=4*x(n)-3*x(n)^2, x(0)=1/10.

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

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A220812 Denominators of the Verhulst sequence x(n+1)=4x(n)-3x(n)^2, x(0)=1/10.

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