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

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

Author

V. Raman, Aug 23 2012

Keywords

• nonn
• frac

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