A086181 Decimal expansion of the bifurcation point B_3, the onset of an 8-cycle in the logistic equation.

3, 5, 4, 4, 0, 9, 0, 3, 5, 9, 5, 5, 1, 9, 2, 2, 8, 5, 3, 6, 1, 5, 9, 6, 5, 9, 8, 6, 6, 0, 4, 8, 0, 4, 5, 4, 0, 5, 8, 3, 0, 9, 9, 8, 4, 5, 4, 4, 4, 5, 7, 3, 6, 7, 5, 4, 5, 7, 8, 1, 2, 5, 3, 0, 3, 0, 5, 8, 4, 2, 9, 4, 2, 8, 5, 8, 8, 6, 3, 0, 1, 2, 2, 5, 6, 2, 5, 8, 5, 6, 6, 4, 2, 4, 8, 9, 1, 7, 9, 9, 9, 6

Offset

1,1

Links

Table of n, a(n) for n=1..102.

D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, Ten Problems in Experimental Mathematics

Eric Weisstein's World of Mathematics, Logistic Map

Formula

A root of the 12th-degree polynomial 4913 + 2108*X^2 - 604*X^3 - 977*X^4 + 8*X^5 + 44*X^6 + 392*X^7 - 193*X^8 - 40*X^9 + 48*X^10 - 12*X^11 + X^12.

Example

3.54409035955192285361596598660480454058309984544457367545781253030584294285\
886301225625856642489179996260899277589974545704537650729751905223146817\
637447928464560949852755537179889159077448053517459045482470711286876373\
464332114219211465412771169565934544669549411924727100000409480552542925\
972401110012866875143607064166969339310061199923409664597323422476443639\
154794410718331803802488512620422107565464513898750258677417630190446728\
9425746174098070947285556077554761795271607917999664978793818256939...

Mathematica

RealDigits[Root[4913+2108*#1^2-604*#1^3-977*#1^4+8*#1^5+44*#1^6+392*#1^7-193*#1^8-40*#1^9+48*#1^10-12*#1^11+#1^12&, 3], 10, 110][[1]]

Crossrefs

Cf. A091517.

Sequence in context: A243296 A081361 A195132 * A000655 A130532 A019707

Adjacent sequences: A086178 A086179 A086180 * A086182 A086183 A086184

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 11 2003

Extensions

More terms from N. J. A. Sloane, Mar 18 2007

Status

approved