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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A040506 Continued fraction for sqrt(530).

Original entry on oeis.org

23, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46
Offset: 0

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Keywords

Examples

			23 + 1/(46 + 1/(46 + 1/(46 + 1/(46 + ...)))) = sqrt(530).
		

Crossrefs

Cf. A040000, A042012/A042013 (convergents).

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(530)),confrac);
  • Mathematica
    Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[530],100]] (* or *) PadRight[{23},100,{46}] (* Harvey P. Dale, Jul 14 2024 *)

Formula

From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 46 for n >= 1.
G.f.: 23*(1+x)/(1-x).
E.g.f.: 46*exp(x) - 23.
a(n) = 23*A040000(n). (End)

A042012 Numerators of continued fraction convergents to sqrt(530).

Original entry on oeis.org

23, 1059, 48737, 2242961, 103224943, 4750590339, 218630380537, 10061748095041, 463059042752423, 21310777714706499, 980758833919251377, 45136217138000269841, 2077246747181931664063, 95598486587506856816739, 4399607629772497345234057
Offset: 0

Views

Author

Keywords

Crossrefs

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[530], 30]] (* Vincenzo Librandi, Nov 13 2013 *)
    LinearRecurrence[{46,1},{23,1059},30] (* Harvey P. Dale, May 05 2016 *)

Formula

From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 46*a(n-1) + a(n-2), n > 1; a(0)=23, a(1)=1059.
G.f.: (23+x)/(1-46*x-x^2). (End)

Extensions

Additional term from Colin Barker, Nov 29 2013
Showing 1-2 of 2 results.