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

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

Offset

0,1

References

Heinz-Otto Peitgen and Peter H. Richter, The Beauty of Fractals, Springer, 1986, p. 23f.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..9

Eric Weisstein's World of Mathematics, Logistic Equation.

Wikipedia, Logistic map.

Formula

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

From Amiram Eldar, Nov 30 2025: (Start)

Sum_{n>=0} 1/a(n) = A036987 (interpreted as a constant).

Product_{n>=0} (1 + 1/a(n)) = 10/9. (End)

Mathematica

a[n_] := 10^(2^n); Array[a, 8, 0] (* Amiram Eldar, Nov 30 2025 *)

Prog

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

Crossrefs

Cf. A000079, A011557, A036987, A051840, A220811 (numerators).

Sequence in context: A173482 A173481 A135651 * A139103 A067217 A266175

Adjacent sequences: A220809 A220810 A220811 * A220813 A220814 A220815

Keyword

nonn,frac,easy

Author

Reinhard Zumkeller, Dec 22 2012

Status

approved