A215758 -id:A215758 - cp's OEIS frontend

A215750 Continued fraction expansion for log_10(6).

0, 1, 3, 1, 1, 32, 1, 1, 278, 1, 1, 2, 5, 1, 4, 1, 3, 7, 1, 1, 44, 1, 4, 2, 1, 1, 2, 8, 2, 1, 5, 1, 1, 4, 3, 1, 9, 17, 1, 1, 12, 2, 1, 1, 80, 3, 10, 1, 2, 63, 3, 3, 2, 1, 1, 16, 2, 5, 3, 2, 1, 2, 12, 3, 1, 5, 4, 191, 165, 1, 6, 5, 28, 1, 1, 4, 1, 3, 1, 5, 2

Offset: 0

V. Raman, Aug 23 2012

Cf. A153496 (decimal expansion), A215754, A215758 (convergents).
Cf. A028232 for the continued fraction expansion for log_2(10).
Cf. A215749 for the continued fraction expansion for log_10(3).
Cf. A082571 for the continued fraction expansion for log_10(7).
Cf. A215752 for the continued fraction expansion for log_10(11).

default(realprecision,99); contfrac(log(6)/log(10))

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

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

V. Raman, Aug 23 2012

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

Numerators are in A215758.

Cf. A046104, A073733, A153496, A215750.

Denominator[Convergents[Log10[6],30]] (* Harvey P. Dale, Mar 22 2019 *)

{my(cf=contfrac(log(6)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[2, 1])}

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

cp's OEIS Frontend

A215750 Continued fraction expansion for log_10(6).

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