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 21-30 of 30 results.

A033167 Positions of the incrementally largest terms in the continued fraction expansion of zeta(3), offset 1 variant.

Original entry on oeis.org

1, 2, 4, 29, 63, 572, 1556, 2013, 2530, 2760, 3019, 4159, 4741, 6820, 10565, 11666, 32859, 139893, 392130, 707970, 1049722, 2081165, 14990404, 36112276, 39552835, 42710787, 199618806
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Positions in this sequence correspond to the n-th term of A013631 at index n-1.
See A229055 for another version.

Links

Crossrefs

Cf. A229055 (= a(n) - 1), A013631 (continued fraction of zeta(3)), A033165, A000023, A033166.

Extensions

More terms from Eric W. Weisstein, Aug 23 2000
More terms from Robert Gerbicz, Aug 22 2006
Edited (with more terms taken from A229055) by N. J. A. Sloane, Jun 16 2021
Edited for offset change in A013631. - Andrew Howroyd, Jul 10 2024

A013687 Continued fraction for zeta(11).

Original entry on oeis.org

1, 2023, 1, 1, 12, 1, 2, 2, 1, 102, 1, 44, 1, 2, 2, 1, 2, 3, 1, 5, 2, 1, 1, 2, 1, 13, 4, 14, 2, 5, 1, 5, 1, 6, 1, 2, 9, 1, 1, 1, 1, 7, 1, 2, 3, 1, 39, 3, 119, 12, 1, 1, 5, 1, 1, 151, 3, 4, 1, 2, 4, 98, 29, 6, 2, 1, 3, 9, 1, 1, 1, 5, 1, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013669.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

Programs

  • Mathematica
    ContinuedFraction[Zeta[11],80] (* Harvey P. Dale, May 22 2013 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A013689 Continued fraction for zeta(13).

Original entry on oeis.org

1, 8149, 13, 1, 2, 1, 6, 23, 3, 1, 7, 1, 1, 5, 1, 1, 4, 1, 1, 1, 4, 1, 1, 2, 2, 8, 1, 29, 32, 22, 2, 123, 1, 2, 1, 10, 1, 2, 2, 1, 4, 1, 13, 5, 8, 34, 2, 1, 7, 1, 2, 1, 3, 20, 8, 1, 4, 1, 5, 1, 59, 3, 7, 1, 1, 3, 2, 6, 1, 1, 2, 9, 1, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013671.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

Programs

  • Mathematica
    ContinuedFraction[Zeta[13],100] (* Harvey P. Dale, Feb 25 2015 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A013690 Continued fraction for zeta(14).

Original entry on oeis.org

1, 16327, 36, 19, 2, 1, 35, 1, 4, 7, 5, 1, 1, 1, 3, 1, 2, 3, 2, 1, 3, 3, 1, 1, 2, 1, 3, 1, 1, 7, 1, 4, 7, 4, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 4, 9, 2, 2, 1, 23, 6, 1, 2, 1, 2, 1, 1, 10, 1, 19, 7, 1, 1, 42, 1, 15, 1, 1, 4, 1, 2, 2, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013672.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696

Programs

  • Mathematica
    ContinuedFraction[Zeta[14],80] (* Harvey P. Dale, Jun 28 2014 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A013691 Continued fraction for zeta(15).

Original entry on oeis.org

1, 32692, 3, 3, 1, 4, 1, 2, 3, 2, 1, 1, 1, 1, 1, 3, 1, 5, 1, 4, 1, 54, 1, 5, 5, 1, 20, 57, 5, 8, 1, 2, 26, 1, 1, 1, 1, 10, 1, 12, 1, 1, 7, 1, 2, 4, 1, 4, 1, 3, 5, 1, 1, 1, 1, 2, 4, 1, 18, 2, 2, 4, 1, 7, 4, 5, 1, 4, 2, 1, 1, 3, 1, 5, 1, 28
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013673.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696

Programs

  • Mathematica
    ContinuedFraction[Zeta[15],80] (* Harvey P. Dale, Jun 01 2012 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A013692 Continued fraction for zeta(16).

Original entry on oeis.org

1, 65435, 2, 1, 5, 1, 4, 1, 3, 3, 1, 7, 1, 2, 6, 2, 1, 7, 1, 1, 2, 1, 4, 4, 2, 3, 13, 1, 2, 1, 5, 1, 1, 8, 1, 5, 1, 1, 1, 4, 1, 2, 2, 2, 1, 44, 1, 2, 1, 2, 4, 2, 1, 6, 153, 41, 1, 26, 1, 4, 1, 3, 3, 1, 1, 1, 5, 6, 15, 4, 7, 1, 1, 1, 2, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013674.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

Programs

  • Mathematica
    ContinuedFraction[Zeta[16],80] (* Harvey P. Dale, Mar 21 2012 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A013693 Continued fraction for zeta(17).

Original entry on oeis.org

1, 130938, 12, 2, 2, 8, 1, 6, 2, 3, 4, 2, 6, 1, 1, 7, 3, 10, 1, 5, 1, 2, 1, 2, 33, 3, 1, 4, 1, 1, 7, 5, 7, 1, 4, 1, 6, 1, 1, 2, 1, 1, 1, 5, 1, 1, 4, 1, 1, 1, 3, 1, 1, 3, 8, 2, 2, 2, 5, 5, 4, 2, 7, 2, 45, 5, 6, 2, 1, 1, 53, 1, 1, 1, 4, 1, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A013675.
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.

Programs

  • Mathematica
    ContinuedFraction[Zeta[17],100] (* Harvey P. Dale, Oct 26 2015 *)

Extensions

Offset changed by Andrew Howroyd, Jul 08 2024

A265824 Continued fraction expansion of the prime zeta function at 3.

Original entry on oeis.org

0, 5, 1, 2, 1, 1, 2, 17, 4, 1, 7, 1, 1, 5, 24, 1, 1, 2, 3, 11, 1, 3, 23, 1, 1, 2, 1, 3, 1, 6, 1, 4, 3, 3, 1, 2, 1, 4, 1, 1, 3, 1, 1, 1, 2, 23, 2, 6, 2, 2, 1, 1, 7, 3, 13, 1, 1, 2, 6, 1, 5, 5, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 28, 2, 1, 4, 10, 3, 2, 1, 1, 2, 1, 3, 1, 1
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 16 2015

Keywords

Comments

Continued fraction of Sum_{n>=1} 1/prime(n)^3 = 0.1747626392994435364231...

Examples

			1/2^3 + 1/3^3 + 1/5^3 +1/7^3 + 1/11^3 + 1/13^3 +... = 1/(5 + 1/(1 + 1/(2 + 1/(1 + 1/(1 + 1/(2 + 1/(17 + 1/(4 + 1/…)))))))).

Links

Crossrefs

Cf. A085541, A013631.

Programs

  • Mathematica
    ContinuedFraction[PrimeZetaP[3], 85]

A269444 Continued fraction expansion of the Dirichlet eta function at 3.

Original entry on oeis.org

0, 1, 9, 6, 2, 1, 1, 1, 1, 1, 1, 6, 1, 4, 1, 7, 2, 1, 1, 1, 2, 91, 32, 1, 1, 6, 23, 1, 1, 1, 1, 2, 9, 1, 2, 1, 1, 5, 1, 1, 37, 12, 1, 12, 3, 2, 87, 1, 4, 2, 2, 2, 320, 1, 7, 1, 2, 6, 3, 1, 6, 4, 1, 4, 2, 1, 69, 1, 4, 3, 3, 1, 14, 3, 1, 3, 1, 10, 2, 694, 2, 4, 21, 1, 1, 1, 3, 3, 10, 2, 1, 2, 2, 1, 3, 5, 1, 3, 9, 1
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Comments

Continued fraction expansion of Sum_{k>=1} (-1)^(k - 1)/k^3 = (3*zeta(3))/4 = 0.901542677369695714...

Examples

			1/1^3 - 1/2^3 + 1/3^3 - 1/4^3 + 1/5^3 - 1/6^3 +... = 1/(1 + 1/(9 + 1/(6 + 1/(2 + 1/(1 + 1/(1 + 1/...)))))).

Links

Crossrefs

Cf. A013631, A197070.

Programs

  • Mathematica
    ContinuedFraction[(3 Zeta[3])/4, 100]

A343244 Position of the first occurrence of an element in the continued fraction of zeta(n) which is larger than the second element.

Original entry on oeis.org

5, 4, 8, 14, 10, 63, 120, 79, 1270, 779, 1749, 3410, 13668, 17704, 20909, 175782, 127426
Offset: 2

Views

Author

Amiram Eldar, Apr 08 2021

Keywords

Comments

a(20) = 111604.
The corresponding values of the a(n)-th elements are 4, 18, 183, 32, 61, 9283, 462, 1483, 3530, 3484, 10812, 8954, ...

Examples

			The continued fraction of zeta(3) is [1; 4, 1, 18, 1, 1, ...]. The first element which is larger than 4 is 18 whose position is 4. Therefore, a(3) = 4.

Crossrefs

Cf. A013697.
Cf. A013679, A013631, A013680, A013681, A013682, A013683, A013684, A013685.

Programs

  • Mathematica
    a[n_] := Module[{c = ContinuedFraction[Zeta[n], 10000]}, FirstPosition[c, _?(# > c[[2]] &)][[1]]]; Array[a, 10, 2]
Previous Showing 21-30 of 30 results.

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

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