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 1-3 of 3 results.

A248280 Egyptian fraction representation of sqrt(55) (A010508) using a greedy function.

Original entry on oeis.org

7, 3, 13, 169, 40134, 1830451404, 6293054590385574716, 99455005060617253985959291400980656073, 14444603640289593121113624113291244368730444113988502168325108818988403980391
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[ 55]]

A010141 Continued fraction for sqrt(55).

Original entry on oeis.org

7, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14, 2, 2, 2, 14
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.41619848709566294871139744... = 7 + 1/(2 + 1/(2 + 1/(2 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 06 2009

Links

Crossrefs

Cf. A010508 Decimal expansion. - Harry J. Smith, Jun 06 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[55],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 23000); x=contfrac(sqrt(55)); for (n=0, 20000, write("b010141.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

A041095 Denominators of continued fraction convergents to sqrt(55).

Original entry on oeis.org

1, 2, 5, 12, 173, 358, 889, 2136, 30793, 63722, 158237, 380196, 5480981, 11342158, 28165297, 67672752, 975583825, 2018840402, 5013264629, 12045369660, 173648439869, 359342249398, 892332938665, 2144008126728, 30908446712857, 63960901552442, 158830249817741
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041094, A010141, A010508, A020812.

Programs

  • Magma
    I:=[1, 2, 5, 12, 173, 358, 889, 2136]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator[Convergents[Sqrt[55], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,178,0,0,0,-1},{1,2,5,12,173,358,889,2136},30] (* Harvey P. Dale, Nov 24 2022 *)

Formula

G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / (x^8-178*x^4+1). - Colin Barker, Nov 12 2013
a(n) = 178*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 12 2013
Showing 1-3 of 3 results.

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

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