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A087089 Periods of logistic map intervals in order of size. 2
1, 2, 4, 8, 3, 6, 16, 6, 5, 12, 10, 12, 32, 12, 10, 4, 5, 7, 24, 24, 20, 20, 8, 8, 7, 24, 10, 14, 9, 64, 24, 10, 16, 14, 20, 8, 18, 14, 9, 48, 48, 14, 20, 40, 6, 48, 16, 9, 40, 40, 7, 18, 48, 16, 20, 16, 28, 18, 9, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The region of stability for period 8 after the point where period 4 splits in two is from 3.5440903596 to 3.5644072661 or a width of .0203169065. The period 3 cycle starts at 3.8284271247 = 1+sqrt(8) and ends at 3.8414990075, a width of .0130718828. This is less than that of period 8 so it follows it in sequence. The logistic map is just the real part of the Mandelbrot set.

The equation f(x)=a*x(1-x), f2(x)=f(f(x)) has a period 3 oscillation whenever 3.82843<a<3.84150.

REFERENCES

For references see A087046.

LINKS

Table of n, a(n) for n=1..60.

CROSSREFS

Sequence in context: A247555 A101942 A050170 * A197382 A246363 A319268

Adjacent sequences:  A087086 A087087 A087088 * A087090 A087091 A087092

KEYWORD

nonn

AUTHOR

Enrico T. Federighi (rico125162(AT)aol.com), Aug 11 2003

STATUS

approved

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Last modified August 20 06:02 EDT 2019. Contains 326139 sequences. (Running on oeis4.)