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 1-5 of 5 results.

A248310 Egyptian fraction representation of sqrt(87) (A010538) using a greedy function.

Original entry on oeis.org

9, 4, 13, 2194, 5329025, 46771207053455, 2802237052080372428026136734, 12510432473074147729999979728187564270491562331166445085, 196800802775232741733342051327922129738105822852379351588232521807086587496995470940763786464334491337080748624
Offset: 0

Views

Author

Robert G. Wilson v, Oct 04 2014

Keywords

Crossrefs

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.
Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Programs

  • Mathematica
    Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 87]]

A040077 Continued fraction for sqrt(87).

Original entry on oeis.org

9, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.3273790530888150455544755... = 9 + 1/(3 + 1/(18 + 1/(3 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 10 2009

Links

Crossrefs

Cf. A010538 Decimal expansion. - Harry J. Smith, Jun 10 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[87],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 36000); x=contfrac(sqrt(87)); for (n=0, 20000, write("b040077.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

A041154 Numerators of continued fraction convergents to sqrt(87).

Original entry on oeis.org

9, 28, 513, 1567, 28719, 87724, 1607751, 4910977, 90005337, 274926988, 5038691121, 15391000351, 282076697439, 861621092668, 15791256365463, 48235390189057, 884028279768489, 2700320229494524, 49489792410669921
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010538, A041155.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[87], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: (9 + 28*x + 9*x^2 - x^3) / (1 - 56*x^2 + x^4). [Bruno Berselli, Oct 29 2013]
a(n) = 56*a(n-2) - a(n-4). [Bruno Berselli, Oct 29 2013]

A176402 Decimal expansion of (9+sqrt(87))/3.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 17 2010

Keywords

Comments

Continued fraction expansion of (9+sqrt(87))/3 is A010725.

Examples

			(9+sqrt(87))/3 = 6.10912635102960501518...

Links

Crossrefs

Cf. A010538 (decimal expansion of sqrt(87)), A010725 (repeat 6, 9).

A176519 Decimal expansion of (9+sqrt(87))/2.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 23 2010

Keywords

Comments

Continued fraction expansion of (9+sqrt(87))/2 is A010725 preceded by 9.

Examples

			(9+sqrt(87))/2 = 9.16368952654440752277...

Crossrefs

Cf. A010538 (decimal expansion of sqrt(87)), A010725 (repeat 6, 9).

Programs

Showing 1-5 of 5 results.

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

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