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 1-4 of 4 results.

A248307 Egyptian fraction representation of sqrt(84) (A010535) using a greedy function.

Original entry on oeis.org

9, 7, 45, 13885, 214285628, 141928437783596058, 34799563546219637107559010387434773, 2746748689148547334068147992469084900474381603247549175076877182361594
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[ 84]]

A040074 Continued fraction for sqrt(84).

Original entry on oeis.org

9, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.1651513899116800131760943... = 9 + 1/(6 + 1/(18 + 1/(6 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 10 2009

Links

Crossrefs

Cf. A010535 Decimal expansion. - Harry J. Smith, Jun 10 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[84],300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 42000); x=contfrac(sqrt(84)); for (n=0, 20000, write("b040074.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

A041148 Numerators of continued fraction convergents to sqrt(84).

Original entry on oeis.org

9, 55, 999, 6049, 109881, 665335, 12085911, 73180801, 1329340329, 8049222775, 146215350279, 885341324449, 16082359190361, 97379496466615, 1768913295589431, 10710859270003201, 194564380155647049, 1178097140203885495, 21400312903825585959
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010535, A041149.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[84], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: -(x^3-9*x^2-55*x-9) / (x^4-110*x^2+1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041149 Denominators of continued fraction convergents to sqrt(84).

Original entry on oeis.org

1, 6, 109, 660, 11989, 72594, 1318681, 7984680, 145042921, 878242206, 15953402629, 96598657980, 1754729246269, 10624974135594, 193004263686961, 1168650556257360, 21228714276319441, 128540936214174006, 2334965566131451549, 14138334333002883300
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041148, A040074, A020841, A010535.

Programs

  • Magma
    I:=[1, 6, 109, 660]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator/@Convergents[Sqrt[84], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[(1 + 6 x - x^2)/(x^4 - 110 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

Formula

G.f.: -(x^2-6*x-1) / (x^4-110*x^2+1). - Colin Barker, Nov 13 2013
a(n) = 110*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013
Showing 1-4 of 4 results.

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

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