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.

A041391 Denominators of continued fraction convergents to sqrt(210).

Original entry on oeis.org

1, 2, 57, 116, 3305, 6726, 191633, 389992, 11111409, 22612810, 644270089, 1311152988, 37356553753, 76024260494, 2166035847585, 4408095955664, 125592722606177, 255593541168018, 7282211875310681, 14820017291789380, 422242696045413321
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041390, A176441, A040195.

Programs

  • Magma
    I:=[1,2,57,116]; [n le 4 select I[n] else 58*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
  • Mathematica
    Denominator[Convergents[Sqrt[210], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Formula

G.f.: -(x^2-2*x-1) / (x^4-58*x^2+1). - Colin Barker, Nov 17 2013
a(n) = 58*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 17 2013

Extensions

More terms from Colin Barker, Nov 17 2013

A176440 Decimal expansion of (14+sqrt(210))/4.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 19 2010

Keywords

Comments

Continued fraction expansion of (14+sqrt(210))/4 is A010728.

Examples

			(14+sqrt(210))/4 = 7.12284418654735964342...

Links

Crossrefs

Cf. A176441 (decimal expansion of sqrt(210)), A010728 (repeat 7, 8).

Programs

  • Mathematica
    RealDigits[(14+Sqrt[210])/4,10,120][[1]]  (* Harvey P. Dale, Apr 13 2011 *)

A040195 Continued fraction for sqrt(210).

Original entry on oeis.org

14, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A176441 (decimal expansion), A041390, A041391 (convergents).

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(210)),confrac);
  • Mathematica
    ContinuedFraction[Sqrt[210], 100] (* or *)
PadRight[{14}, 100, {28, 2}] (* Paolo Xausa, Sep 17 2024 *)

A178331 Decimal expansion of (17+2*sqrt(210))/29.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 25 2010

Keywords

Comments

Continued fraction expansion of (17+2*sqrt(210))/29 is A135265.

Examples

			(17+2*sqrt(210))/29 = 1.58561218939237507404...

Crossrefs

Cf. A176441 (decimal expansion of sqrt(210)), A135265 (repeat 1, 1, 1, 2, 2, 2).

Programs

  • Mathematica
    RealDigits[(17+2Sqrt[210])/29,10,120][[1]] (* Harvey P. Dale, Apr 05 2019 *)

A176457 Decimal expansion of (28+2*sqrt(210))/7.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 20 2010

Keywords

Comments

Continued fraction expansion of (28+2*sqrt(210))/7 is A010728 preceded by 8.
a(n) = A171539(n-1) for n > 1.

Examples

			(28+2*sqrt(210))/7 = 8.14039335605412530677...

Crossrefs

Cf. A171539 (decimal expansion of sqrt(6/35)), A176441 (decimal expansion of sqrt(210)), A010728 (repeat 7, 8).

Programs

  • Mathematica
    RealDigits[(28+2Sqrt[210])/7,10,120][[1]] (* Harvey P. Dale, Apr 07 2018 *)
Showing 1-5 of 5 results.

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

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