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 21-26 of 26 results.

A155979 Decimal expansion of log_10 (24).

Original entry on oeis.org

1, 3, 8, 0, 2, 1, 1, 2, 4, 1, 7, 1, 1, 6, 0, 6, 0, 2, 2, 9, 3, 6, 2, 4, 4, 5, 8, 7, 4, 2, 8, 5, 9, 4, 3, 8, 9, 5, 0, 4, 6, 9, 8, 5, 0, 8, 5, 7, 7, 0, 2, 1, 4, 8, 8, 7, 6, 1, 1, 4, 8, 0, 2, 3, 6, 8, 6, 5, 5, 3, 7, 2, 0, 6, 0, 6, 9, 3, 4, 6, 5, 1, 5, 0, 3, 7, 5, 0, 1, 1, 2, 0, 0, 2, 1, 7, 4, 8, 1
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3802112417116060229362445874285943895046985085770214887611...

Links

Crossrefs

Cf. decimal expansion of log_10(m): A007524 (m=2), A114490 (m=3), A114493 (m=4), A153268 (m=5), A153496 (m=6), A153620 (m=7), A153790 (m=8), A104139 (m=9), A154182 (m=11), A154203 (m=12), A154368 (m=13), A154478 (m=14), A154580 (m=15), A154794 (m=16), A154860 (m=17), A154953 (m=18), A155062 (m=19), A155522 (m=20), A155677 (m=21), A155746 (m=22), A155830 (m=23).

Programs

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

A385659 Decimal expansion of log_10(1 + 1/3).

Original entry on oeis.org

1, 2, 4, 9, 3, 8, 7, 3, 6, 6, 0, 8, 2, 9, 9, 9, 5, 3, 1, 3, 2, 4, 4, 9, 8, 8, 6, 1, 9, 3, 8, 7, 0, 7, 4, 4, 3, 3, 6, 2, 5, 0, 8, 9, 8, 7, 3, 3, 5, 2, 1, 2, 1, 7, 7, 9, 0, 9, 8, 9, 2, 8, 1, 9, 4, 8, 9, 8, 7, 2, 2, 5, 7, 6, 5, 1, 8, 7, 8, 9, 5, 9, 3, 0, 8, 8, 6
Offset: 0

Views

Author

Marco Ripà, Jul 06 2025

Keywords

Comments

Probability that 3 occurs as the first significant digit in data collections according to Benford's law (see A007524).

Examples

			0.12493873660829995313244988619...

Links

Crossrefs

Benford's law for digit: A007524 (1), A104140 (9), A154203 (5), A154580 (2).

Programs

  • Mathematica
    RealDigits[Log[10, 4/3], 10, 90][[1]]

Formula

Equals A114493 - A114490. - R. J. Mathar, Jul 13 2025

Extensions

a(16) to a(86) corrected by Marco Ripà, Jul 12 2025

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])}

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

A114473 Number of decimal digits in the 10^n-th Motzkin number.

Original entry on oeis.org

1, 4, 45, 473, 4766, 47705, 477113, 4771203
Offset: 0

Views

Author

Eric W. Weisstein, Nov 30 2005

Keywords

Links

Crossrefs

Cf. A001006, A114490.

Formula

Lim_{n->oo} log_10(a(n))/n = log_10(3) = 0.477121254719662437295027903... since the real root possessing the smallest absolute value of expression (1-2*x-3*x^2) (found in the g.f.) equals 1/3. - Paul D. Hanna, Dec 01 2005

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010
More terms from Eric Rowland, Oct 23 2015
Previous Showing 21-26 of 26 results.

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

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