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.

Previous Showing 11-14 of 14 results.

A181919 The value of r at the bifurcation point 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, 3, 8, 4, 9, 8, 0, 3, 2, 9, 4, 7, 3, 0, 2, 7, 1, 7, 2, 8, 9, 8, 8, 1, 5, 7, 7, 3, 5, 7, 8, 2, 1, 1, 6, 7, 5, 6, 9, 1, 5, 0, 3, 3, 2, 5, 1, 5, 9, 3, 9, 6, 9, 6, 3, 4, 9, 5, 7, 8, 3, 3, 0, 7, 5, 2, 8, 5, 7, 4, 5, 0, 9, 8, 2, 6, 2, 4, 8, 2, 1, 0, 6, 9, 0, 5, 1, 7, 2, 2, 2, 4, 0, 3, 8
Offset: 1

Views

Author

Cheng Zhang, Apr 01 2012

Keywords

Comments

Root of a degree 4095*2 = 8190 polynomial.

Examples

			3.6797038498...

Links

Crossrefs

Cf. A086178, A086179, A086180, A086181, A091517, A118452, A181906, A181907, A181909, A181910, A181911, A181912, A181913, A181915, A181916, A181917, A181918.

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]]

A087046 Algebraic order of r_n, the value of r in the logistic map that corresponding to the onset of the period 2^n-cycle.

Original entry on oeis.org

1, 2, 12, 240, 65280, 4294901760, 18446744069414584320, 340282366920938463444927863358058659840, 115792089237316195423570985008687907852929702298719625575994209400481361428480
Offset: 1

Views

Author

Eric W. Weisstein, Aug 04 2003

Keywords

Links

Crossrefs

Cf. A086180, A086181, A087089, A118454, A000215, A346192.
Cf. A051179 (partial sums).

Programs

  • Mathematica
    Table[If[n <= 1, 1, 2^(2^(n - 1)) - 2^(2^(n - 2))], {n, 1, 10}] (* Cheng Zhang, Apr 02 2012 *)
  • PARI
    a(n) = 1<<(1<<(n-1)) - 1<<(1<<(n-2)); \\ Kevin Ryde, Jan 18 2024

Formula

a(n) = 2^(2^(n - 1)) - 2^(2^(n - 2)) with n>1, a(1)=1. - Cheng Zhang, Apr 02 2012
Sum_{n>=1} 1/a(n) = 1 + A346192. - Amiram Eldar, Jul 18 2021

Extensions

More terms from Cheng Zhang, Apr 03 2012
Previous Showing 11-14 of 14 results.

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