A091517 -id:A091517 - cp's OEIS frontend

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

Eric W. Weisstein, Jul 11 2003

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

D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, Ten Problems in Experimental Mathematics
Eric Weisstein's World of Mathematics, Logistic Map

Cf. A091517.

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]]

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.

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

A118452 Decimal expansion of onset of logistic map 5-bifurcation.

Original entry on oeis.org

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

Offset: 1

Eric W. Weisstein, Apr 28 2006

Algebraic of order 22.

			3.7381723752659623694...

Eric Weisstein's World of Mathematics, Logistic Map

Cf. A086178, A086180, A091517, A098587, A118453, A118454.

RealDigits[Root[ -28629151 - 31399714*#1 - 14329471*#1^2 + 3613360*#1^3 + 13369804*#1^4 + 5836984*#1^5 - 1495060*#1^6 - 4002880*#1^7 - 1613676*#1^8 + 1484268*#1^9 + 808298*#1^10 - 234632*#1^11 - 294146*#1^12 + 8008*#1^13 + 103556*#1^14 - 17344*#1^15 - 18092*#1^16 + 7488*#1^17 + 116*#1^18 - 700*#1^19 + 189*#1^20 - 22*#1^21 + #1^22 &, 4],10,110][[1]]

A181906 The value of r at the onset of the first period-9 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 240*2 = 480 polynomial.

			3.6871968733...

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181917, A181918, A181919.

A181907 The value of r at the onset of the first period-10 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 472*2 = 944 polynomial.

			3.60520806689...

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A181906, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181917, A181918, A181919.

A181909 The r value at the onset of the first period-11 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 1013*2 = 2026 polynomial.

			3.6817160193...

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181910, A181911, A181912, A181913, A181915, A181916, A181917, A181918, A181919.

A181910 The value of r at the onset of the first period-12 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 1959*2 = 3918 polynomial.

			3.58202300107...

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181911, A181912, A181913, A181915, A181916, A181917, A181918, A181919

A181911 The value of r at the onset of the first period-13 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 4083*2 = 9166 polynomial.

			3.6797024577659...

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181912, A181913, A181915, A181916, A181917, A181918, A181919

A118453 Decimal expansion of onset of logistic map 6-bifurcation.

Original entry on oeis.org

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

Offset: 1

Eric W. Weisstein, Apr 28 2006

Algebraic of order 40.

			3.6265531616949737258...

Eric Weisstein's World of Mathematics, Logistic Map

Cf. A086178, A086180, A091517, A098587, A118454.

RealDigits[Root[3063651608241 + 583552687284*#1 + 1847916843066*#1^2 - 195203691396*#1^3 - 266965430067*#1^4 - 930539982708*#1^5 - 32353949026*#1^6 - 20846657216*#1^7 + 268499651644*#1^8 + 203273817100*#1^9 - 70347416426*#1^10 - 23477492116*#1^11 - 148805533357*#1^12 + 63425976316*#1^13 + 29299283358*#1^14 + 1219753488*#1^15 + 10442067223*#1^16 - 25709485160*#1^17 + 5757007476*#1^18 + 945192256*#1^19 + 3195434424*#1^20 + 746246488*#1^21 - 3839476860*#1^22 + 1483852216*#1^23 + 347099271*#1^24 - 126361652*#1^25 - 100717898*#1^26 - 75365092*#1^27 + 137026587*#1^28 - 48885412*#1^29 - 12966642*#1^30 + 16770304*#1^31 - 5563348*#1^32 + 195228*#1^33 + 516582*#1^34 - 225060*#1^35 + 52181*#1^36 - 7676*#1^37 + 722*#1^38 - 40*#1^39 + #1^40 &, 5],10,110][[1]]

A181915 The value of r at the bifurcation point of the first period-9 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 252*2 = 504 polynomial.

			3.6872742105...

Cheng Zhang, the minimal polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181916, A181917, A181918, A181919.

A181916 The value of r at the bifurcation point of the first period-10 cycle of the logistic map f(x) = rx(1 - x).

Original entry on oeis.org

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

Offset: 1

Cheng Zhang, Apr 01 2012

Root of a degree 495*2 = 990 polynomial.

			3.605916932....

Cheng Zhang, the polynomial for T = r*(r-2)

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181917, A181918, A181919.

cp's OEIS Frontend

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

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A118452 Decimal expansion of onset of logistic map 5-bifurcation.

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A181906 The value of r at the onset of the first period-9 cycle of the logistic map f(x) = r*x*(1 - x).

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A181907 The value of r at the onset of the first period-10 cycle of the logistic map f(x) = r*x*(1 - x).

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A181909 The r value at the onset of the first period-11 cycle of the logistic map f(x) = r*x*(1 - x).

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A181910 The value of r at the onset of the first period-12 cycle of the logistic map f(x) = r*x*(1 - x).

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A181911 The value of r at the onset of the first period-13 cycle of the logistic map f(x) = r*x*(1 - x).

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A118453 Decimal expansion of onset of logistic map 6-bifurcation.

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A181915 The value of r at the bifurcation point of the first period-9 cycle of the logistic map f(x) = r*x*(1 - x).

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A181906 The value of r at the onset of the first period-9 cycle of the logistic map f(x) = rx(1 - x).

A181907 The value of r at the onset of the first period-10 cycle of the logistic map f(x) = rx(1 - x).

A181909 The r value at the onset of the first period-11 cycle of the logistic map f(x) = rx(1 - x).

A181910 The value of r at the onset of the first period-12 cycle of the logistic map f(x) = rx(1 - x).

A181911 The value of r at the onset of the first period-13 cycle of the logistic map f(x) = rx(1 - x).

A181915 The value of r at the bifurcation point of the first period-9 cycle of the logistic map f(x) = rx(1 - x).

A181916 The value of r at the bifurcation point of the first period-10 cycle of the logistic map f(x) = rx(1 - x).