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 1-10 of 13 results. Next

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

A073733 Numerators of convergents to log_2(10).

Original entry on oeis.org

1, 3, 10, 93, 196, 485, 2136, 13301, 28738, 42039, 70777, 254370, 325147, 6107016, 6432163, 44699994, 51132157, 146964308, 198096465, 345060773, 1578339557, 1923400330, 82361153417, 496090320832, 578451474249, 2809896217828, 6198243909905, 21404627947543
Offset: 0

Views

Author

Joseph Myers, Sep 01 2002

Keywords

Comments

This power of two is closer to some power of ten than any previous power of two. - Robert G. Wilson v, Aug 22 2013

Links

Crossrefs

Denominators are A046104. Continued fraction expansion is A028232.

Programs

  • Mathematica
    Join[{1},Numerator[Convergents[Log[2,10],40]]] (* Harvey P. Dale, Jun 22 2014 *)

Extensions

More terms from Harvey P. Dale, Jun 22 2014

A046103 Numerators of convergents to the diesis, log_2(5/4).

Original entry on oeis.org

0, 1, 9, 19, 47, 207, 1289, 2785, 4074, 6859, 24651, 31510, 591831, 623341, 4331877, 4955218, 14242313, 19197531, 33439844, 152956907, 186396751, 7981620449, 48076119445, 56057739894, 272307079021, 600671897936
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Links

Crossrefs

Cf. A046104, A116985.

Programs

  • Mathematica
    Numerator[ Table[ ContinuedFraction[ Log[ 5/4 ]/Log[ 2 ], i ]//Normal, {i, 30} ] ]
  • PARI
    contfracpnqn(contfrac(log(5/4)/log(2)),99)[1,] \\ M. F. Hasler, Apr 30 2020

Extensions

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

A215753 Denominators of the continued fraction convergents of log_10(3).

Original entry on oeis.org

1, 2, 21, 44, 109, 153, 2098, 2251, 17855, 323641, 665137, 1653915, 2319052, 6292019, 21195109, 91072455, 112267564, 203340019, 2959027830, 6121395679, 272300437706, 278421833385, 1107565937861, 1385987771246, 20511394735305, 42408777241856, 105328949219017, 147737726460873
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

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

Crossrefs

Numerators are in A215757.
Cf. A114490, A215749.
Cf. A046104, A073733.

Programs

  • Mathematica
    Denominator[Convergents[Log[10,3],30]] (* Harvey P. Dale, Jan 24 2015 *)
  • PARI
    {my(cf=contfrac(log(3)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[2, 1])}

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

A215756 Denominators of the continued fraction convergents of log_10(11).

Original entry on oeis.org

1, 24, 145, 459, 1063, 1522, 2585, 9277, 11862, 21139, 33001, 318148, 351149, 1371595, 1722744, 3094339, 4817083, 22362671, 27179754, 103901933, 131081687, 3643107482, 3774189169, 14965674989, 78602564114, 93568239103, 265739042320, 890785366063, 37678724416966, 339999305118757, 377678029535723
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

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

Crossrefs

Numerators are in A215760.
Cf. A046104, A073733, A154182, A215752.

Programs

  • PARI
    {my(cf=contfrac(log(11)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[2, 1])}

Extensions

Offset changed by Andrew Howroyd, Jul 09 2024

A215757 Numerators of the continued fraction convergents of log_10(3).

Original entry on oeis.org

0, 1, 10, 21, 52, 73, 1001, 1074, 8519, 154416, 317351, 789118, 1106469, 3002056, 10112637, 43452604, 53565241, 97017845, 1411815071, 2920647987, 129920326499, 132840974486, 528443249957, 661284224443, 9786422392159, 20234129008761, 50254680409681, 70488809418442, 120743489828123, 311975789074688
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

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

Crossrefs

Denominators are in A215753.
Cf. A046104, A073733, A114490, A215749.

Programs

  • Mathematica
    Rest[Numerator[Convergents[Log[10,3],30]]] (* Harvey P. Dale, Sep 02 2015 *)
  • PARI
    {my(cf=contfrac(log(3)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[1, 1])}

Extensions

a(0)=0 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

A215760 Numerators of the continued fraction convergents of log_10(11).

Original entry on oeis.org

1, 25, 151, 478, 1107, 1585, 2692, 9661, 12353, 22014, 34367, 331317, 365684, 1428369, 1794053, 3222422, 5016475, 23288322, 28304797, 108202713, 136507510, 3793905483, 3930412993, 15585144462, 81856135303, 97441279765, 276738694833, 927657364264
Offset: 0

Views

Author

V. Raman, Aug 23 2012

Keywords

Comments

11^(Denominators of convergents) get increasingly closer to 10^a(n), approximately a(n) digits.

Crossrefs

Denominators are in A215756.
Cf. A046104, A073733, A154182, A215752.

Programs

  • Mathematica
    Convergents[Log10[11],30]//Numerator (* Harvey P. Dale, Dec 20 2024 *)
  • PARI
    {my(cf=contfrac(log(11)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[1, 1])}

Extensions

Offset changed by Andrew Howroyd, Jul 09 2024
Showing 1-10 of 13 results. Next

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

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