A215758 Numerators of the continued fraction convergents of log_10(6).

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

Author

V. Raman, Aug 23 2012

Keywords

• nonn
• frac

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