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 1-4 of 4 results.

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

Views

Author

N. J. A. Sloane

Keywords

Examples

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

Links

Crossrefs

Cf. A013662 (zeta(4)). - Harry J. Smith, Apr 29 2009
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013681-A013696.

Programs

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

Extensions

Offset changed by Andrew Howroyd, Jul 09 2024

A244110 Continued fraction expansion of the prime zeta function at 5.

Original entry on oeis.org

0, 27, 1, 30, 2, 1, 5, 1, 3, 2, 2, 7, 1, 2, 12, 1, 1, 23, 1, 3, 1, 6, 1, 3, 16, 1, 1, 1, 4, 3, 3, 5, 1, 2, 1, 1, 7, 5, 1, 3, 1, 1, 1, 28, 14, 3, 3, 1, 6, 18, 11, 7, 1, 29, 1, 1, 2, 10, 1, 6, 1, 1, 8, 2, 303, 3, 1, 2, 1, 61, 1, 11, 1, 10, 10, 1, 1, 2, 1, 1, 45, 19, 1, 1, 1, 6, 1, 1, 2, 4, 1
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 16 2015

Keywords

Comments

Continued fraction of Sum_{n>=1} 1/prime(n)^5 = 0.0357550174839242571328...

Examples

			1/2^5 + 1/3^5 + 1/5^5 +1/7^5 + 1/11^5 + 1/13^5 +... = 1/(27 + 1/(1 + 1/(30 + 1/(2 + 1/(1 + 1/(5 + 1/(1 + 1/(3 + 1/...)))))))).

Links

Crossrefs

Cf. A013681, A085965.

Programs

  • Mathematica
    ContinuedFraction[PrimeZetaP[5], 90]

A269482 Continued fraction expansion of the Dirichlet eta function at 5.

Original entry on oeis.org

0, 1, 34, 1, 6, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 35, 3, 1, 5, 4, 1, 2, 2, 1, 4, 1, 1, 1, 2, 10, 2, 1, 6, 9, 23, 1, 5, 1, 1, 1, 1, 1, 2, 1, 3, 4, 1, 2, 1, 1, 2, 2, 1, 1, 5, 4, 7, 1, 1, 1, 1, 2, 2, 1, 4, 1, 1, 2, 8, 3, 2, 1, 3, 1, 5, 356, 2, 57, 6, 1, 6, 1, 1, 31, 1, 5, 1, 1, 477, 1, 9, 7, 3, 4
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 27 2016

Keywords

Comments

Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^5 = (15*zeta(5))/16 = 0.9721197704469093...

Examples

			1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 +... = 1/(1 + 1/(34 + 1/(1 + 1/(6 + 1/(1 + 1/(1 + 1/...)))))).

Links

Crossrefs

Cf. A013681, A267316.

Programs

  • Mathematica
    ContinuedFraction[(15 Zeta[5])/16, 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]
Showing 1-4 of 4 results.

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

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