A215753 -id:A215753 - cp's OEIS frontend

A215749 Continued fraction expansion of log_10(3).

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

V. Raman, Aug 23 2012

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)).

ContinuedFraction[Log10[3],120] (* Harvey P. Dale, Nov 24 2017 *)

default(realprecision,99); contfrac(log(3)/log(10))

a(0)=0 prepended 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

V. Raman, Aug 23 2012

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

Denominators are in A215753.

Cf. A046104, A073733, A114490, A215749.

Rest[Numerator[Convergents[Log[10,3],30]]] (* Harvey P. Dale, Sep 02 2015 *)

{my(cf=contfrac(log(3)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[1, 1])}

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

cp's OEIS Frontend

A215749 Continued fraction expansion of log_10(3).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Extensions