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 1-3 of 3 results.

A046104 Denominators of convergents to the diesis log_2(5/4).

Original entry on oeis.org

1, 3, 28, 59, 146, 643, 4004, 8651, 12655, 21306, 76573, 97879, 1838395, 1936274, 13456039, 15392313, 44240665, 59632978, 103873643, 475127550, 579001193, 24793177656, 149338067129, 174131244785, 845863046269, 1865857337323
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

Also denominators of convergents to log_2(5), cf. A020858. Denominators of convergents to log_2(128/125), sometimes also referred to as diesis, are (1, 29, 117, 263, 643, 906, 1549, 5553, 7102, 90777, ...). - M. F. Hasler, Apr 30 2020

Links

Crossrefs

Cf. A046103 (numerators corresponding to log_2(5/4)), A116985 (numerators corresponding to log_2(5)).

Programs

  • Mathematica
    Denominator[ Table[ ContinuedFraction[ Log[ 5/4 ]/Log[ 2 ], i ]//Normal, {i, 30} ] ]
Denominator[Convergents[Log[2,5/4],30]] (* Harvey P. Dale, Jan 24 2015 *)
  • PARI
    contfracpnqn(contfrac(log(5)/log(2)),99)[2,] \\ M. F. Hasler, Apr 30 2020

Extensions

Name corrected and links edited by M. F. Hasler, Apr 30 2020

A116985 Numerators of the convergents to log_2(5).

Original entry on oeis.org

2, 7, 65, 137, 339, 1493, 9297, 20087, 29384, 49471, 177797, 227268, 4268621, 4495889, 31243955, 35739844, 102723643, 138463487, 241187130, 1103212007, 1344399137, 57567975761, 346752253703, 404320229464, 1964033171559
Offset: 1

Views

Author

Gene Ward Smith, Mar 27 2006

Keywords

Crossrefs

Cf. A046103, A046104, A112732.

Programs

  • Mathematica
    FromContinuedFraction /@ Reverse[NestList[Most, ContinuedFraction[Log[2, 5], 20], 19]] // InputForm (* Eric W. Weisstein, Apr 07 2006 *)

Extensions

Corrected by Eric W. Weisstein, Apr 07 2006

A116984 Duplicate of A046104.

Original entry on oeis.org

1, 3, 28, 59, 146, 643, 4004, 8651, 12655, 21306, 76573, 97879, 1838395, 1936274, 13456039, 15392313, 44240665, 59632978, 103873643, 475127550, 579001193, 24793177656, 149338067129, 174131244785, 845863046269, 1865857337323
Offset: 1

Views

Author

Gene Ward Smith, Mar 27 2006

Keywords

Comments

This sequence defines equal divisions of the octave with especially accurate values for the major third, 5/4. This sequence is related to A112732, denominators of the convergents for the continued fraction for log_2(5)/4.
Duplicate of A046104.

Crossrefs

Cf. A116985, A046103, A046104, A112732.

Programs

  • Mathematica
    Table[Denominator[FromContinuedFraction[ContinuedFraction[Log[2, 5], n]]], {n, 1, 40}] (* Stefan Steinerberger, Apr 08 2006 *)
  • PARI
    contfracpnqn(contfrac(log(5)/log(2)), 99)[2, ] \\ M. F. Hasler, Apr 30 2020

Extensions

More terms from Stefan Steinerberger, Apr 08 2006
Showing 1-3 of 3 results.

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

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