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.

Previous Showing 11-17 of 17 results.

A040132 Continued fraction for sqrt(145).

Original entry on oeis.org

12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).

Links

Crossrefs

Cf. A041264/A041265 (convergents), A176910 (decimal expansion).
Cf. A040000, A040002, A040006.

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[145],300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)

Formula

From Elmo R. Oliveira, Feb 12 2024: (Start)
a(n) = 24 for n >= 1.
G.f.: 12*(1+x)/(1-x).
E.g.f.: 24*exp(x) - 12.
a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)

A040306 Continued fraction for sqrt(325).

Original entry on oeis.org

18, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			18 + 1/(36 + 1/(36 + 1/(36 + 1/(36 + ...)))) = sqrt(325).

Links

Crossrefs

Cf. A041612/A041613 (convergents).
Cf. A040000, A040002, A040006.

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(325)),confrac);
  • Mathematica
    Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[325],100]] (* or *) PadRight[{18},100,{36}] (* Harvey P. Dale, Dec 01 2020 *)

Formula

From Elmo R. Oliveira, Feb 14 2024: (Start)
a(n) = 36 for n >= 1.
G.f.: 18*(1+x)/(1-x).
E.g.f.: 36*exp(x) - 18.
a(n) = 18*A040000(n) = 9*A040002(n) = 6*A040006(n). (End)

A040210 Continued fraction for sqrt(226).

Original entry on oeis.org

15, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			15 + 1/(30 + 1/(30 + 1/(30 + 1/(30 + ...)))) = sqrt(226).

Links

Crossrefs

Cf. A041420/A041421 (convergents).
Cf. A040000, A040006, A040020.

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(226)),confrac);

Formula

From Elmo R. Oliveira, Feb 13 2024: (Start)
a(n) = 30 for n >= 1.
G.f.: 15*(1+x)/(1-x).
E.g.f.: 30*exp(x) - 15.
a(n) = 15*A040000(n) = 5*A040006(n) = 3*A040020(n). (End)

A040420 Continued fraction for sqrt(442).

Original entry on oeis.org

21, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).

Links

Crossrefs

Cf. A041840/A041841 (convergents).
Cf. A040000, A040006, A040042.

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(442)),confrac);
  • Mathematica
    Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[442],120]] (* or *) PadRight[{21},120,{42}] (* Harvey P. Dale, Nov 28 2024 *)

Formula

From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 42 for n >= 1.
G.f.: 21*(1+x)/(1-x).
E.g.f.: 42*exp(x) - 21.
a(n) = 21*A040000(n) = 7*A040006(n) = 3*A040042(n). (End)

A040552 Continued fraction for sqrt(577).

Original entry on oeis.org

24, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			24 + 1/(48 + 1/(48 + 1/(48 + 1/(48 + ...)))) = sqrt(577).

Links

Crossrefs

Cf. A042104/A042105 (convergents).
Cf. A040000, A040002, A040006.

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(577)),confrac);

Formula

From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 48 for n >= 1.
G.f.: 24*(1+x)/(1-x).
E.g.f.: 48*exp(x) - 24.
a(n) = 24*A040000(n) = 12*A040002(n) = 8*A040006(n). (End)

A040702 Continued fraction for sqrt(730).

Original entry on oeis.org

27, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			27 + 1/(54 + 1/(54 + 1/(54 + 1/(54 + ...)))) = sqrt(730).

Links

Crossrefs

Cf. A042404/A042405 (convergents).
Cf. A040000, A040006, A040072.

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(730)),confrac);

Formula

From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 54 for n >= 1.
G.f.: 27*(1+x)/(1-x).
E.g.f.: 54*exp(x) - 27.
a(n) = 27*A040000(n) = 9*A040006(n) = 3*A040072(n). (End)

A040930 Continued fraction for sqrt(962).

Original entry on oeis.org

31, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			31 + 1/(62 + 1/(62 + 1/(62 + 1/(62 + ...)))) = sqrt(962).

Links

Crossrefs

Cf. A042860/A042861 (convergents).
Continued fraction for sqrt(a^2+1) = (a, 2a, 2a, 2a....): A040000 (contfrac(sqrt(2)) = (1,2,2,...)), A040002, A040006, A040012, A040020, A040030, A040042, A040056, A040072, A040090, A040110 (contfrac(sqrt(122)) = (11,22,22,...)), A040132, A040156, A040182, A040210, A040240, A040272, A040306, A040342, A040380, A040420 (contfrac(sqrt(442)) = (21,42,42,...)), A040462, A040506, A040552, A040600, A040650, A040702, A040756, A040812, A040870 (contfrac(sqrt(901)) = (30,60,60,...)).

Programs

  • Maple
    with(numtheory): Digits := 300: convert(evalf(sqrt(962)),confrac);
  • Mathematica
    PadRight[{31},100,62] (* Harvey P. Dale, Sep 18 2012 *)

Formula

G.f.: 31*(1+x)/(1-x). - Colin Barker, Aug 11 2012
From Elmo R. Oliveira, Feb 16 2024: (Start)
a(n) = 62 for n >= 1.
E.g.f.: 62*exp(x) - 31.
a(n) = 31*A040000(n). (End)
Previous Showing 11-17 of 17 results.

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

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