A013696 -id:A013696 - cp's OEIS frontend

A013631 Continued fraction for zeta(3).

1, 4, 1, 18, 1, 1, 1, 4, 1, 9, 9, 2, 1, 1, 1, 2, 7, 1, 1, 7, 11, 1, 1, 1, 3, 1, 6, 1, 30, 1, 4, 1, 1, 4, 1, 3, 1, 2, 7, 1, 3, 1, 2, 2, 1, 16, 1, 1, 3, 3, 1, 2, 2, 1, 6, 1, 1, 1, 6, 1, 1, 4, 428, 5, 1, 1, 3, 1, 1, 11, 2, 4, 4, 5, 4, 1, 5, 14, 1, 3, 1, 2, 19, 1, 2, 5, 1, 7, 1, 1, 1, 1, 1, 57, 3, 2, 14, 2

Offset: 0

N. J. A. Sloane, John Morrison (John.Morrison(AT)armltd.co.uk)

			zeta(3) = 1.2020569031595942... = 1 + 1/(4 + 1/(1 + 1/(18 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 20 2009

Harry J. Smith, Table of n, a(n) for n = 0..19999
Eric Weisstein's World of Mathematics, Apery's Constant.
G. Xiao, Contfrac.
Index entries for continued fractions for constants.
Index entries for zeta function.

Cf. A002117 (decimal expansion), A078984, A078985 (convergents).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013680-A013696.

Mathematica
```
ContinuedFraction[ Zeta[3], 100]
```

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(zeta(3)); for (n=1, 20000, write("b013631.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 20 2009

Offset changed by Andrew Howroyd, Jul 10 2024

A013679 Continued fraction for zeta(2) = Pi^2/6.

Original entry on oeis.org

1, 1, 1, 1, 4, 2, 4, 7, 1, 4, 2, 3, 4, 10, 1, 2, 1, 1, 1, 15, 1, 3, 6, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 5, 1, 2, 2, 1, 1, 6, 27, 20, 3, 97, 105, 1, 1, 1, 1, 1, 45, 2, 8, 19, 1, 4, 1, 1, 3, 1, 2, 1, 1, 1, 5, 1, 1, 2, 3, 6, 1, 1, 1, 2, 1, 5, 1, 1, 2, 9, 5, 3, 2, 1, 1, 1

Offset: 0

N. J. A. Sloane

			1.644934066848226436472415166... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...))))

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.

T. D. Noe, Table of n, a(n) for n = 0..9999
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for zeta function.

Cf. A013661 (decimal expansion).

Cf. continued fractions for zeta(3)-zeta(20): A013631, A013680-A013696.

Mathematica
```
ContinuedFraction[ Pi^2/6, 100]
```

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^2/6); for (n=1, 20000, write("b013679.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 29 2009

Offset changed by Andrew Howroyd, Jul 10 2024

A013680 Continued fraction for zeta(4).

Original entry on oeis.org

1, 12, 6, 1, 3, 1, 4, 183, 1, 1, 2, 1, 3, 1, 1, 5, 4, 2, 7, 23, 1, 1, 1, 1, 3, 2, 4, 2, 2, 22, 1, 13, 5, 1, 4, 2, 1, 3, 1, 1, 1, 6, 11, 40, 1, 7, 5, 2, 4, 1, 2, 3, 14, 9, 1, 33, 78, 1, 12, 4, 1, 2, 551, 1, 1, 1, 1, 1, 1, 2, 1, 9, 2, 7, 3, 1, 3, 2, 15, 1, 1, 2, 2

Offset: 0

N. J. A. Sloane

			zeta(4) = 1 + 1/(12 + 1/(6 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, Apr 29 2009

T. D. Noe, Table of n, a(n) for n = 0..9999
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for zeta function

Cf. A013662 (zeta(4)). - Harry J. Smith, Apr 29 2009

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013681-A013696.

ContinuedFraction[Zeta[4],80] (* Harvey P. Dale, Oct 13 2013 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^4/90); for (n=1, 20000, write("b013680.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 29 2009

Offset changed by Andrew Howroyd, Jul 09 2024

A013681 Continued fraction for zeta(5).

Original entry on oeis.org

1, 27, 12, 1, 1, 15, 1, 5, 1, 2, 19, 1, 1, 32, 1, 13, 1, 1, 1, 3, 1, 3, 2, 16, 1, 12, 4, 1, 5, 1, 1, 1, 1, 1, 2, 2, 6, 1, 8, 8, 6, 2, 3, 2, 2, 1, 30, 1, 17, 116, 1, 7, 1, 1, 1, 1, 1, 1, 2, 2, 12, 1, 4, 1, 1, 94, 1, 1, 3, 3, 6, 6, 1, 1, 2, 1, 17, 1, 1, 7, 1, 1, 11

Offset: 0

N. J. A. Sloane

Cf. A013663 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[5],80] (* Harvey P. Dale, Nov 30 2012 *)

Offset changed by Andrew Howroyd, Jul 09 2024

A013682 Continued fraction for zeta(6).

Original entry on oeis.org

1, 57, 1, 1, 1, 15, 1, 6, 3, 61, 1, 5, 3, 1, 6, 1, 3, 3, 6, 1, 10, 1, 3, 2, 1, 4, 1, 1, 5, 1, 61, 1, 3, 1, 2, 1, 3, 2, 1, 3, 1, 2, 2, 28, 1, 2, 18, 53, 2, 1, 17, 11, 3, 4, 3, 5, 2, 1, 27, 9, 8, 3, 3, 3, 9, 5, 1, 3, 29, 1, 4, 1, 2, 40, 4, 8, 1, 3, 1, 2, 2, 1, 4

Offset: 0

N. J. A. Sloane

Cf. A013664 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[6],100] (* Harvey P. Dale, Jul 19 2019 *)

Offset changed by Andrew Howroyd, Jul 09 2024

A013683 Continued fraction for zeta(7).

Original entry on oeis.org

1, 119, 1, 3, 2, 1, 2, 1, 39, 2, 3, 12, 3, 1, 1, 1, 2, 6, 5, 1, 5, 1, 2, 1, 23, 2, 1, 5, 34, 2, 1, 1, 3, 47, 2, 1, 8, 16, 1, 4, 1, 2, 1, 1, 1, 10, 72, 1, 1, 1, 1, 1, 2, 3, 13, 1, 2, 1, 5, 1, 27, 2, 9283, 1, 36, 1, 1, 1, 1, 3, 3, 23, 27, 5, 2, 4, 1, 3, 16, 1, 4

Offset: 0

N. J. A. Sloane

Cf. A013665 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[7],100] (* Harvey P. Dale, Sep 13 2020 *)

Offset changed by Andrew Howroyd, Jul 09 2024

A013684 Continued fraction for zeta(8).

Original entry on oeis.org

1, 245, 3, 1, 8, 4, 2, 3, 2, 1, 1, 4, 1, 3, 12, 2, 2, 34, 1, 1, 1, 1, 4, 9, 1, 56, 3, 38, 1, 1, 6, 1, 1, 1, 1, 3, 2, 1, 1, 5, 9, 3, 1, 11, 2, 3, 1, 5, 2, 2, 1, 4, 1, 27, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 72, 17, 1, 36, 1, 5, 6, 1, 4, 10, 1, 4, 1, 4, 1, 1, 1, 8

Offset: 0

N. J. A. Sloane

Cf. A013666 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[8],80] (* Harvey P. Dale, Aug 14 2020 *)

Offset changed by Andrew Howroyd, Jul 09 2024

A013685 Continued fraction for zeta(9).

Original entry on oeis.org

1, 497, 1, 10, 5, 1, 1, 8, 3, 2, 2, 1, 2, 1, 2, 5, 4, 2, 49, 1, 3, 3, 1, 1, 2, 1, 2, 30, 4, 1, 17, 3, 8, 2, 1, 2, 1, 1, 10, 6, 9, 2, 3, 1, 22, 1, 2, 1, 1, 2, 1, 1, 2, 18, 1, 1, 1, 9, 1, 2, 9, 1, 5, 2, 4, 1, 5, 1, 2, 2, 2, 6, 1, 8, 1, 5, 1, 4, 1483, 1, 3, 1, 2, 7

Offset: 0

N. J. A. Sloane

Cf. A013667 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[9],100] (* Harvey P. Dale, Aug 05 2023 *)

Offset changed by Andrew Howroyd, Jul 09 2024

A013695 Continued fraction for zeta(19).

Original entry on oeis.org

1, 524050, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 2, 5, 14, 1, 5, 1, 3, 1, 3, 1, 3, 2, 1, 1, 1, 4, 1, 9, 1, 2, 1, 6, 2, 1, 1, 1, 76, 85, 1, 8, 1, 1, 7, 12, 7, 2, 1, 2, 4, 1, 3, 1, 22, 1, 3, 6, 1, 1, 1, 1, 1, 4, 1, 11, 1, 3, 1, 2, 1, 6, 1, 9, 1, 2

Offset: 0

N. J. A. Sloane

Cf. A013677 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[19], 100] (* Paolo Xausa, Jul 03 2024 *)

Offset changed by Andrew Howroyd, Aug 10 2024

A013686 Continued fraction for zeta(10).

Original entry on oeis.org

1, 1005, 2, 4, 1, 98, 7, 11, 2, 1, 1, 6, 2, 3, 28, 1, 37, 1, 2, 7, 9, 13, 85, 4, 3, 34, 5, 3, 7, 4, 7, 1, 3, 2, 1, 22, 1, 1, 1, 1, 3, 15, 1, 9, 12, 1, 3, 3, 3, 1, 3, 2, 1, 2, 1, 1, 2, 10, 8, 2, 2, 11, 54, 4, 5, 1, 2, 2, 1, 3, 2, 1, 19, 4, 5, 1, 2, 2, 7, 1, 200

Offset: 0

N. J. A. Sloane

Cf. A013668 (decimal expansion).

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

ContinuedFraction[Zeta[10], 100] (* Paolo Xausa, Jul 03 2024 *)

Offset changed by Andrew Howroyd, Jul 09 2024

cp's OEIS Frontend

A013631 Continued fraction for zeta(3).

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A013679 Continued fraction for zeta(2) = Pi^2/6.

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A013680 Continued fraction for zeta(4).

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A013681 Continued fraction for zeta(5).

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A013682 Continued fraction for zeta(6).

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A013683 Continued fraction for zeta(7).

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A013684 Continued fraction for zeta(8).

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A013685 Continued fraction for zeta(9).

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