cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 240*2 = 480 polynomial.

Examples

			3.6871968733...

Links

Crossrefs

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181907, 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) = r*x*(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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 1013*2 = 2026 polynomial.

Examples

			3.6817160193...

Links

Crossrefs

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) = r*x*(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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 1959*2 = 3918 polynomial.

Examples

			3.58202300107...

Links

Crossrefs

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) = r*x*(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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 4083*2 = 9166 polynomial.

Examples

			3.6797024577659...

Links

Crossrefs

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

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).

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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 252*2 = 504 polynomial.

Examples

			3.6872742105...

Links

Crossrefs

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) = r*x*(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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 495*2 = 990 polynomial.

Examples

			3.605916932....

Links

Crossrefs

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

A181917 The value of r at the bifurcation point of the first period-11 cycle of the logistic map f(x) = r*x*(1 - x).

Original entry on oeis.org

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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 1023*2 = 2046 polynomial.

Examples

			3.68172664565...

Links

Crossrefs

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181918, A181919.

A181912 The value of r at the bifurcation point of the first period-5 cycle of the logistic map f(x) = r*x*(1 - x).

Original entry on oeis.org

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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 15*2 = 30 polynomial.

Examples

			3.7411207566...

Crossrefs

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181913, A181915, A181916, A181917, A181918, A181919.

Programs

  • Mathematica
    RealDigits[1 + Sqrt[1 + T] /. NSolve[1291467969 - 313083144 T + 149426046 T^2 - 88548768 T^3 + 58697100 T^4 - 26978787 T^5 + 11351480 T^6 - 4444924 T^7 + 1519712 T^8 - 462764 T^9 + 118147 T^10 - 24008 T^11 + 3838 T^12 - 448 T^13 + 32 T^14 - T^15 == 0, T, Reals, WorkingPrecision -> 200][[1]][[1]]][[1]]

A181913 The value of r at the bifurcation point of the first period-7 cycle of the logistic map f(x) = r*x*(1 - x).

Original entry on oeis.org

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

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 63*2 = 126 polynomial.

Examples

			3.702154928...

Crossrefs

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911, A181912, A181915, A181916, A181917, A181918, A181919.

Programs

  • Mathematica
    RealDigits[1 + Sqrt[1 + T] /.  NSolve[97862157334118736160267353892330031361 - 24275883989858911295570196314376441888 T + 11949756847721247033090755550100031472 T^2 - 7305759525507048491687489710934851842 T^3 + 4979912078948645588349153608449721856 T^4 - 3626559126667087845228068253830569728 T^5 + 2762422187660818660072532819743957008 T^6 - 1880399068065596812679449750312116489 T^7 + 1211937495049324668386707923551814144 T^8 - 759866924055411176816609501610145824 T^9 + 466557599052858501899389873590498576 T^10 - 280965824140635821336538113950238208 T^11 + 165486490562715543623266844910996960 T^12 - 95328733468347624721143436596991728 T^13 + 53730737569188242850960902675061540 T^14 - 29631735433275573295736684905520448 T^15 + 15982002519220233506297359288643328 T^16 - 8426732734596962888735943308790072 T^17 + 4341578043750972227945942898034432 T^18 - 2184193663643426076323203313845088 T^19 + 1072045107586559381111681621669072 T^20 - 512897616845631175409335289338708 T^21 + 239007878643078614755697662563584 T^22 - 108415793383957757795350567428064 T^23 + 47846270482094728117141329426032 T^24 - 20533661180243125068599265318144 T^25 + 8564906198781819799124804441280 T^26 - 3470264291680473250164651552944 T^27 + 1364870535759255877272510765950 T^28 - 520676891296255096870756895040 T^29 + 192488968788190123648373004064 T^30 - 68893036110679144584159460492 T^31 + 23845858487001866959614915840 T^32 - 7973063091544280406837942464 T^33 + 2572118763623299179804574640 T^34 - 799578831968317708137874814 T^35 + 239196982314145129630174464 T^36 - 68763448836715397230901728 T^37 + 18967378806716848507574128 T^38 - 5011787964028065103857408 T^39 + 1266306625250424841996640 T^40 - 305348843999288091901136 T^41 + 70117811645069434371412 T^42 - 15296768944400171831616 T^43 + 3162019501419003256064 T^44 - 617525327585232743224 T^45 + 113570706028361676288 T^46 - 19599347048769496032 T^47 + 3161153679144274672 T^48 - 474387152691155748 T^49 + 65902567592614400 T^50 - 8426269030832672 T^51 + 984947439372048 T^52 - 104425099694592 T^53 + 9947578647040 T^54 - 841756889488 T^55 + 62385936393 T^56 - 3978343968 T^57 + 213336304 T^58 - 9328642 T^59 + 318464 T^60 - 7936 T^61 + 128 T^62 - T^63 == 0, T, Reals, WorkingPrecision -> 200][[1]][[1]]][[1]]

A118454 Algebraic degree of the onset of the logistic map n-bifurcation.

Original entry on oeis.org

1, 1, 2, 2, 22, 40, 114, 12, 480, 944, 2026, 3918, 8166, 16104, 32630, 240, 131038, 260928, 524250, 1046418, 2096706, 4190168, 8388562, 16768200, 33554240, 67092432, 134216136, 268402446, 536870854, 1073672968, 2147483586, 65280, 8589928346, 17179606976, 34359737478
Offset: 1

Views

Author

Eric W. Weisstein, Apr 28 2006

Keywords

Comments

a(2^n) is A087046(n).

Examples

			The onsets begin at 1, 3, 1+2*sqrt(2), 1+sqrt(6), ...

Links

Crossrefs

Cf. A000740, A006876, A086178, A086180, A087046, A091517, A098587, A118452, A118453, A118746, A181906, A181907, A181909, A181910, A181911.

Programs

  • Mathematica
    degRp[n_] := Sum[MoebiusMu[n/d] 2^(d - 1), {d, Divisors[n]}]; degRo[n_] := degRp[n]*2 - Sum[EulerPhi[n/d] degRp[d], {d, Divisors[n]}]; Table[If[n <= 2, 1, 2 If[2^Round[Log2[n]] == n, degRp[n/2], degRo[n]]], {n, 1, 35}] (* Cheng Zhang, Apr 02 2012 *)

Extensions

More terms from Cheng Zhang, Apr 02 2012
Showing 1-10 of 10 results.

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