A215759 Numerators of the continued fraction convergents of log_10(7).

0, 1, 5, 11, 60, 371, 431, 2074774, 2075205, 4149979, 10375163, 24900305, 60175773, 85076078, 145251851, 230327929, 1527219425, 7866425054, 9393644479, 787538916811, 5522166062156, 11831871041123, 17354037103279, 29185908144402, 46539945247681, 401505470125850, 2054067295876931

Offset: 0

Author

V. Raman, Aug 23 2012

Keywords

• nonn
• frac

Comments

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

Crossrefs

Denominators are in A215755.

Cf. A046104, A073733, A082571, A153620.

Programs

Mathematica

Rest[Numerator[Convergents[Log[10,7],30]]] (* Harvey P. Dale, Feb 16 2014 *)

PARI

{my(cf=contfrac(log(7)/log(10))); vector(#cf, i, contfracpnqn( cf[1..i])[1, 1])}

Extensions

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