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 25 results. Next

A144984 Denominators of an Egyptian fraction for 1/sqrt(5) (A020762).

Original entry on oeis.org

3, 9, 362, 148807, 432181530536, 615828580117398011389583, 385329014801969222669766835659574445455872858297
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Links

Crossrefs

Cf. A020762, A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003.

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[5], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a

A145003 Denominators of an Egyptian fraction for 1/sqrt(29) = 0.185695338... (A020786).

Original entry on oeis.org

6, 53, 6221, 891830563, 950677235679298964, 2245647960428048728674383451656707058, 11636905679093503238901947768600244923435901955366623291532461461126244496
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Crossrefs

Cf. A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003.

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[29], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a

A006890 Decimal expansion of Feigenbaum bifurcation velocity.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Colin Mallows, Jeffrey Shallit

Keywords

Comments

"... These are related to properties of dynamical systems with 'period-doubling' oscillations. The ratio of successive differences between period-doubling bifurcation parameters approaches the number 4.669... Period doubling has been discovered in many physical systems before they enter the chaotic regime. Feigenbaum numbers have not been proved to be transcendental but are generally believed to be. ..." [Pickover]
The Feigenbaum delta constant is the convergence ratio {g(k)-g(k-1)}/{g(k+1)-g(k)} of successive period-doubling thresholds g(k) in the continuous map x(n+1)=f(x(n),g) of an interval onto itself. - Lekraj Beedassy, Jan 07 2005
The above statement is only valid for functions f satisfying some properties, e.g., having a single locally quadratic maximum. See, e.g., the MathWorld link for more details. - M. F. Hasler, May 01 2018
Named after the American mathematical physicist Mitchell Jay Feigenbaum (1944-2019). - Amiram Eldar, Jun 16 2021

Examples

			4.669201609102990671853203820466201617258185577475768632745651343004134...

References

  • Michael F. Barnsley, Fractals Everywhere, New Edition, Prof. of Math., Australian National University, Dover Publications, Inc., Mineola, NY, 2012, page 314.
  • John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 24, 208.
  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 65-76
  • Clifford A. Pickover, (1993) 'The fifteen most famous transcendental numbers.' "Journal of Recreational Mathematics," 25(1):12.
  • Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Chapter 44, 'The 15 Most Famous Transcendental Numbers,' Oxford University Press, Oxford, England, 2000, pages 103 - 106.
  • Clifford A. Pickover, The Math Book, Sterling, NY, 2009; see p. 462.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • Ian Stewart, Nature's Numbers, Chapter 8, Do Dice Play God?, Weidenfeld & Nicolson, 1995.

Links

Crossrefs

Cf. A159766 and A069544 (continued fraction), A069261 (Egyptian fraction), A108952 (1/delta), A102817 (Gamma(delta^2)).
Cf. A006891 (Feigenbaum reduction parameter), A218453.

Extensions

Additional comments from Robert G. Wilson v, Dec 29 2000

A159766 Continued fraction expansion of the Feigenbaum constant A006890 = 4.66920160910...

Original entry on oeis.org

4, 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, 1, 33, 1, 1, 53, 1, 1, 1, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 239, 1, 3, 31, 1, 1, 11, 1, 13, 123, 2, 2, 2, 2, 13, 15, 1, 2, 3, 3, 1, 3, 1, 1, 6, 1, 3, 1, 1, 13, 8, 1, 7, 1, 2, 1, 8, 7, 1, 17, 1, 6, 1, 1, 3, 1, 1, 13, 1, 1, 4, 2, 9, 124, 1, 1, 3
Offset: 0

Views

Author

Harry J. Smith, Apr 21 2009

Keywords

Comments

Feigenbaum bifurcation velocity delta. See A006890 for further information.
Apart from the first term, the same as A069544. - R. J. Mathar, Apr 28 2009

Examples

			4.66920160910299067185320382... = 4 + 1/(1 + 1/(2 + 1/(43 + 1/(2 + ...))))

Links

Crossrefs

Cf. A006890 (decimal expansion of the constant), A069544 (continued fraction of the fractional part), A069261 (Egyptian fraction).

Programs

  • Mathematica
    fbvd = (* copy value from the link in A006890 or immediately above *); ContinuedFraction@ fbvd (* Robert G. Wilson v, Apr 27 2009 *)
  • PARI
    { default(realprecision,1019); delta=4.\
6692016091029906718532038204662016172581855774757686327456513430\
0413433021131473713868974402394801381716598485518981513440862714\
2027932522312442988890890859944935463236713411532481714219947455\
6443658237932020095610583305754586176522220703854106467494942849\
8145339172620056875566595233987560382563722564800409510712838906\
1184470277585428541980111344017500242858538249833571552205223608\
7250291678860362674527213399057131606875345083433934446103706309\
4520191158769724322735898389037949462572512890979489867683346116\
2688911656312347446057517953912204556247280709520219819909455858\
1946136877445617396074115614074243754435499204869180982648652368\
4387027996490173977934251347238087371362116018601281861020563818\
1835409759847796417390032893617143215987824078977661439139576403\
7760537119096932066998361984288981837003229412030210655743295550\
3888458497370347275321219257069584140746618419819610061296401614\
8771294441590140546794180019813325337859249336588307045999993837\
5411726563553016862529032210862320550634510679399023341675; A159766=contfrac(delta); for (n=1, 967, write("b159766.txt", n-1, " ", A159766[n])); } \\ Harry J. Smith, May 15 2009
  • PARI
    A159766=contfrac(delta) \\ M. F. Hasler, Apr 30 2018

Extensions

Old PARI program deleted by Harry J. Smith, May 19 2009

A144983 Denominators of greedy Egyptian fraction for 1/sqrt(3) (A020760).

Original entry on oeis.org

2, 13, 2341, 41001128, 3352885935529869, 17147396444547741051849884001699, 1847333322606272250132077006229901193256553492442739965269739579
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Links

Crossrefs

Cf. A001466, A006487, A006524, A006525, A006526, A020760, A069139, A069261, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A144984-A145003.

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[3], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a

A142725 Denominators of an Egyptian fraction for 1/Sqrt[17] = 0.242535625...

Original entry on oeis.org

5, 24, 1151, 6727710, 97954001297811, 12083213443785578998604325741, 2111557350230332542969297514824119073134312726162508784857, 5126406954746155312559668571658555244727150562238830979161154018392336359308299948544053564102183773577991816755308
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Crossrefs

A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[17], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)

A142726 Denominators of an Egyptian fraction for 1/Sqrt[20] = 0.2236067977...

Original entry on oeis.org

5, 43, 2850, 9380555, 131539825706327, 25568462906010064277774504354, 1702783284378767791750994476557209698496292570221862357616, 9282809298390896944529722953873240985108041182275536393531898614770319137100914187360035180181565645720539192811580
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Crossrefs

A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[20], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)

A144985 Denominators of an Egyptian fraction for 1/Sqrt[6]=0.408248290463863...

Original entry on oeis.org

3, 14, 287, 484228, 624850913463, 832896370765715143490072, 7620764031777359266114991754446899201236457828088, 74466937067918173179787895367258766085493130434332689333832927329763999409894621431449951498850730
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Crossrefs

A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[6], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)

A144986 Denominators of an Egyptian fraction for 1/Sqrt[7]=0.377964473...

Original entry on oeis.org

3, 23, 868, 1242123, 2776290405248, 11161696107523243223922840, 261638153821481209775970282548980739821715625184617, 189055393361766552088064316219614698328133697744770641431804048878604165927723712902309210241320415402
Offset: 1

Views

Author

Artur Jasinski, Oct 07 2008

Keywords

Crossrefs

A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[7], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)

A144987 Denominators of an Egyptian fraction for 1/sqrt(8) = 0.35355339059327376223...

Original entry on oeis.org

3, 50, 4545, 28362567, 1497340447522680, 4387088233067304774404776830059, 21181904263756953142587802868501086598875135541314844201016311, 850362874661071143418760124561686027269498941223459043945221634054718647025769989728300760240990642339926562157579631197188
Offset: 1

Views

Author

Artur Jasinski, Sep 28 2008

Keywords

Crossrefs

Cf. A069139, A006487, A006526, A006525, A006524, A001466, A110820, A117116, A118323, A118324, A118325, A144835, A132480-A132574, A069261, A144984-A145003.

Programs

  • Mathematica
    a = {}; k = N[1/Sqrt[8], 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (*Artur Jasinski*)
Showing 1-10 of 25 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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