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.

A215749 Continued fraction expansion of log_10(3).

Original entry on oeis.org

0, 2, 10, 2, 2, 1, 13, 1, 7, 18, 2, 2, 1, 2, 3, 4, 1, 1, 14, 2, 44, 1, 3, 1, 14, 2, 2, 1, 1, 2, 30, 1, 1, 3, 2, 4, 3, 7, 2, 6, 8, 1, 2, 7, 62, 1, 3, 4, 60, 1, 89, 3, 3, 1, 1, 7, 3, 3, 2, 4, 2, 2, 1, 25, 2, 6, 2, 2, 1, 3, 2, 2, 1, 1, 2, 5, 1, 1, 1, 1, 1, 3, 66
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Crossrefs

Cf. A114490 (decimal expansion), A215753, A215757 (convergents).
Cf. A028232, A215750, A082571, A215752 (continued fraction expansion of log_2(10), log_10(6), log_10(7), log_10(11)).

Programs

  • Mathematica
    ContinuedFraction[Log10[3],120] (* Harvey P. Dale, Nov 24 2017 *)
  • PARI
    default(realprecision,99); contfrac(log(3)/log(10))

Extensions

a(0)=0 prepended by Andrew Howroyd, Jul 09 2024

A215752 Continued fraction expansion for log_10(11).

Original entry on oeis.org

1, 24, 6, 3, 2, 1, 1, 3, 1, 1, 1, 9, 1, 3, 1, 1, 1, 4, 1, 3, 1, 27, 1, 3, 5, 1, 2, 3, 42, 9, 1, 2, 1, 2, 26, 1, 1, 2, 1, 1, 2, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 20, 1, 2, 1, 1, 1, 4, 1, 2, 5, 9, 2, 1, 1, 2, 68, 3, 1, 2, 5, 3, 2, 21, 1, 2, 39, 1, 3, 1, 2, 1, 1, 3, 5
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Crossrefs

Cf. A154182 (decimal expansion), A215756, A215760 (convergents).
Cf. A028232 for the continued fraction expansion for log_2(10).
Cf. A215749 for the continued fraction expansion for log_10(3).
Cf. A215750 for the continued fraction expansion for log_10(6).
Cf. A082571 for the continued fraction expansion for log_10(7).

Programs

  • PARI
    default(realprecision,99); contfrac(log(11)/log(10))

A215754 Denominators of the continued fraction convergents of log_10(6).

Original entry on oeis.org

1, 1, 4, 5, 9, 293, 302, 595, 165712, 166307, 332019, 830345, 4483744, 5314089, 25740100, 31054189, 118902667, 863372858, 982275525, 1845648383, 82190804377, 84036452760, 418336615417, 920709683594, 1339046299011, 2259755982605, 5858558264221, 49128222096373, 104115002456967, 153243224553340
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

6^a(n) gets increasingly close to 10^(numerator of convergent).

Crossrefs

Numerators are in A215758.
Cf. A046104, A073733, A153496, A215750.

Programs

  • Mathematica
    Denominator[Convergents[Log10[6],30]] (* Harvey P. Dale, Mar 22 2019 *)
  • PARI
    {my(cf=contfrac(log(6)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[2, 1])}

Extensions

a(0)=1 prepended by Andrew Howroyd, Jul 09 2024

A215758 Numerators of the continued fraction convergents of log_10(6).

Original entry on oeis.org

0, 1, 3, 4, 7, 228, 235, 463, 128949, 129412, 258361, 646134, 3489031, 4135165, 20029691, 24164856, 92524259, 671834669, 764358928, 1436193597, 63956877196, 65393070793, 325529160368, 716451391529, 1041980551897, 1758431943426, 4558844438749, 38229187453418, 81017219345585, 119246406799003
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

6^(denominator of convergent) gets increasingly close to 10^a(n), agreeing to approximately a(n) digits

Crossrefs

Denominators are in A215754.
Cf. A046104, A073733, A153496, A215750.

Programs

  • Mathematica
    Rest[Convergents[Log10[6],30]]//Numerator (* Harvey P. Dale, Sep 05 2020 *)
  • PARI
    {my(cf=contfrac(log(6)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[1, 1])}

Extensions

a(0)=0 prepended by Andrew Howroyd, Jul 09 2024
Showing 1-4 of 4 results.

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