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.

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A224230 Egyptian fraction expansion of Pi.

Original entry on oeis.org

3, 8, 61, 5020, 128541455, 162924332716605980, 28783052231699298507846309644849796, 871295615653899563300996782209332544845605756266650946342214549769447
Offset: 0

Views

Author

N. J. A. Sloane, Apr 11 2013, following a suggestion from Anthony C Robin

Keywords

Comments

A variant of A001466, which is the main entry.

Examples

			Pi = 3 + 1/8 + 1/61 + 1/5020 + ...

Crossrefs

Cf. A001466, A182257.

A001467 Denominators of an expansion for Pi.

Original entry on oeis.org

1, 1, 1, 7, -791, -3748629, 151648960887729, -1323497544567561138595307148089, 41444465282455711991644958522615049159671653083333293470875123
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			a(4) = -791 since Pi - (1/1) - (1/1) - (1/1) - (1/7) = -0.001264489... is closer to 1/(-791) = -0.001264222... than to 1/(-790) = -0.0012658228...

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A001466, A014013, A073422.

Programs

  • PARI
    x=Pi; for(k=0,8,if(x<1,d=round(1/x),d=1); x=x-1/d; print(d,", ")) \\ Jaume Oliver Lafont, Feb 21 2009

Formula

Numerators are 1.

Extensions

Edited by Henry Bottomley, Jul 30 2002

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

A243020 Denominators of Egyptian fraction expansion of Pi, without repetition.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 27, 744, 1173268, 2586625801171, 14348276635209672362238685, 1062286904072440687703470835520966381484062674280821
Offset: 1

Views

Author

Arlu Genesis A. Padilla, May 29 2014

Keywords

Comments

Slightly different version of A182257, disregarding the repetition of values.

Examples

			Pi = 1 + 1/2 + 1/3 + ... + 1/12 + 1/27 + 1/744 + ...

Links

Crossrefs

Cf. A182257, A001466, A224230

Extensions

a(16)-a(18) from Arlu Genesis A. Padilla, Jul 30 2018

A052385 a(n)*10^n are the denominators of the greedy alternating Egyptian fraction expansion of Pi - 3 of the form Sum_{n>=0} (-1)^n / (a(n)*10^n).

Original entry on oeis.org

7, 79, 7498, 5830114, 8652011824287, 13597204960705459608723126, 34810495772672927583903155370200945603822050731477, 1443540369391032855921234984363709782471552979298036142515612532020988429757781997263178546460721652
Offset: 0

Views

Author

Boris Gourevitch (sai1042(AT)ensai.fr), Mar 10 2000

Keywords

Examples

			Pi = 3 + 1/7 - 1/(10 * 79) + 1/(10^2 * 7498) - 1/(10^3 * 5830114) + ...

Links

Crossrefs

Cf. A000796, A001466, A014013.

Programs

  • Mathematica
    s={}; x = Pi - 3; Do[a = Floor[1/((-10)^k * x)]; AppendTo[s, a]; x-=1/((-10)^k*a), {k, 0, 7}]; s (* Amiram Eldar, Jan 23 2019 *)

Formula

a(n) = floor((-1)^n/(s(n-1)*10^n)), where s(n) = Pi - 3 - Sum_{k=0..n} (-1)^k/(a(k)*10^k).

Extensions

a(6)-a(10) from Amiram Eldar, Jan 23 2019

A156736 Signed greedy Egyptian fraction for Pi/2.

Original entry on oeis.org

1, 2, 14, -1582, -7497258, 303297921775458, -2646995089135122277190614296178, 82888930564911423983289917045230098319343306166666586941750246
Offset: 0

Views

Author

Jaume Oliver Lafont, Feb 14 2009

Keywords

Comments

The second and fourth convergents of Pi (22/7 and 355/113) appear when truncating the series to three and four terms.

Examples

			1+1/2+1/14=11/7=(1/2)(22/7)
1+1/2+1/14-1/1582=355/226=(1/2)(355/113)

Links

Crossrefs

Cf. A001466, A156269, A156618.
Cf. A156750. [From Jaume Oliver Lafont, Mar 03 2009]

Programs

  • PARI
    x=Pi/2; for (k=0,7, d=round(1/x); x=x-1/d; print1(d,", "))

Formula

Sum(n>=0,1/a(n))=Pi/2.
a(n) = 2*A001467(n+1). - R. J. Mathar, Apr 02 2011

A156750 Greedy Egyptian fraction for Pi/2.

Original entry on oeis.org

1, 2, 15, 243, 69282, 36600664305, 6435072487994269232829, 364103502021384610224777078613738432189483892
Offset: 0

Views

Author

Jaume Oliver Lafont, Feb 14 2009

Keywords

Links

Crossrefs

Cf. A001466, A156269, A156736.

Programs

  • PARI
    x=Pi/2; for (k=0, 7, d=ceil(1/x); x=x-1/d; print(d,", "))

Formula

Sum(n>=0,1/a(n))=Pi/2

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*)
Previous Showing 11-20 of 37 results. Next

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

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