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 21-28 of 28 results.

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

A076590 First occurrence of n as a term in the continued fraction for zeta(2)=Pi^2/6.

Original entry on oeis.org

1, 6, 12, 5, 37, 23, 8, 56, 83, 14, 107, 128, 111, 121, 20, 171, 346, 172, 57, 45, 607, 641, 968, 925, 239, 291, 44, 659, 396, 233, 186, 1353, 509, 739, 843, 681, 1020, 213, 577, 345, 670, 196, 287, 91, 54, 3510, 910, 800, 3462, 803, 503, 355, 3428, 1157, 247
Offset: 1

Views

Author

Benoit Cloitre, Oct 20 2002

Keywords

Crossrefs

Cf. A013679, A032523.

Programs

  • Mathematica
    Module[{nn=4000,cf},cf=ContinuedFraction[Pi^2/6,nn];Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Dec 29 2024 *)
  • PARI
    /* 15000 precision digits */ v=contfrac(zeta(2)); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

A265823 Continued fraction expansion of the prime zeta function at 2.

Original entry on oeis.org

0, 2, 4, 1, 2, 1, 3, 1, 1, 33, 1, 8, 3, 3, 4, 1, 1, 2, 1, 38, 2, 29, 12, 4, 1, 6, 1, 1, 1, 5, 4, 9, 4, 2, 2, 5, 1, 3, 1, 1, 1, 7, 9, 1, 7, 1, 201, 5, 1, 17, 4, 1, 19, 5, 2, 56, 1, 5, 1, 16, 4, 1, 1, 12, 63, 1, 5, 9, 1, 1, 18, 26, 1, 1, 5, 4, 3, 1, 1, 13, 2, 3, 3, 1, 1
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 16 2015

Keywords

Comments

Continued fraction of Sum_{n>=1} 1/prime(n)^2 = 0.4522474200410654985065...

Examples

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

Links

Crossrefs

Cf. A085548, A013679.

Programs

  • Mathematica
    ContinuedFraction[PrimeZetaP[2], 84]

A269443 Continued fraction expansion of the Dirichlet eta function at 2.

Original entry on oeis.org

0, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 4, 1, 1, 1, 1, 1, 1, 4, 1, 6, 3, 7, 1, 7, 3, 3, 2, 4, 2, 2, 1, 1, 2, 1, 1, 3, 2, 1, 5, 1, 3, 1, 2, 1, 1, 13, 40, 1, 1, 1, 48, 211, 4, 91, 1, 16, 9, 1, 10, 8, 2, 4, 1, 2, 3, 2, 1, 1, 13, 3, 1, 2, 2, 1, 3, 1, 18, 2, 1, 1, 1, 5, 3, 7, 1, 1, 21, 1, 6, 4, 1, 1, 2, 1, 3, 2
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Comments

Continued fraction expansion of Sum_{k>=1} (-1)^(k-1)/k^2 = Zeta(2)/2 = Pi^2/12 = 0.8224670334241132182362...

Examples

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

Links

Crossrefs

Cf. A013679, A072691.

Programs

  • Mathematica
    ContinuedFraction[Pi^2/12, 100]
  • PARI
    contfrac(Pi^2/12) \\ Michel Marcus, Feb 26 2016

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 21-28 of 28 results.

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

Content is available under The OEIS End-User License Agreement.