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 1-2 of 2 results.

A040156 Continued fraction for sqrt(170).

Original entry on oeis.org

13, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			13 + 1/(26 + 1/(26 + 1/(26 + 1/(26 + ...)))) = sqrt(170).

Links

Crossrefs

Cf. A040000, A041312/A041313 (convergents).

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[170],300] (* Vladimir Joseph Stephan Orlovsky, Mar 25 2011*)

Formula

From Elmo R. Oliveira, Feb 12 2024: (Start)
a(n) = 26 for n >= 1.
G.f.: 13*(1+x)/(1-x).
E.g.f.: 26*exp(x) - 13.
a(n) = 13*A040000(n). (End)

A041312 Numerators of continued fraction convergents to sqrt(170).

Original entry on oeis.org

13, 339, 8827, 229841, 5984693, 155831859, 4057613027, 105653770561, 2751055647613, 71633100608499, 1865211671468587, 48567136558791761, 1264610762200054373, 32928446953760205459, 857404231559965396307, 22325438467512860509441, 581318804386894338641773
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041313.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[170], 30]] (* Vincenzo Librandi, Nov 01 2013 *)

Formula

From Philippe Deléham, Nov 21 2008: (Start)
a(n) = 26*a(n-1) + a(n-2) for n > 1, a(0)=13, a(1)=339.
G.f.: (13+x)/(1-26*x-x^2). (End)

Extensions

More terms from Colin Barker, Nov 06 2013
Showing 1-2 of 2 results.

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

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