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

%I A086181 #13 Feb 16 2025 08:32:50
%S A086181 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,
%T A086181 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,
%U A086181 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
%N A086181 Decimal expansion of the bifurcation point B_3, the onset of an 8-cycle in the logistic equation.
%H A086181 D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, <a href="http://eprints.cecm.sfu.ca/archive/00000270/">Ten Problems in Experimental Mathematics</a>
%H A086181 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogisticMap.html">Logistic Map</a>
%F A086181 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.
%e A086181 3.54409035955192285361596598660480454058309984544457367545781253030584294285\
%e A086181 886301225625856642489179996260899277589974545704537650729751905223146817\
%e A086181 637447928464560949852755537179889159077448053517459045482470711286876373\
%e A086181 464332114219211465412771169565934544669549411924727100000409480552542925\
%e A086181 972401110012866875143607064166969339310061199923409664597323422476443639\
%e A086181 154794410718331803802488512620422107565464513898750258677417630190446728\
%e A086181 9425746174098070947285556077554761795271607917999664978793818256939...
%t A086181 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]]
%Y A086181 Cf. A091517.
%K A086181 nonn,cons
%O A086181 1,1
%A A086181 _Eric W. Weisstein_, Jul 11 2003
%E A086181 More terms from _N. J. A. Sloane_, Mar 18 2007