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A254351 Numerators of increasingly better rational approximations to log(3)/log(2) with increasing denominators.

%I A254351 #22 Feb 23 2015 14:50:30
%S A254351 2,3,5,8,11,19,46,65,84,317,401,485,569,1054,13133,14187,15241,16295,
%T A254351 17349,18403,19457,20511,21565,22619,23673,24727,50508,125743,176251,
%U A254351 301994,8632083,8934077,9236071,9538065,9840059,10142053,10444047,10746041,11048035
%N A254351 Numerators of increasingly better rational approximations to log(3)/log(2) with increasing denominators.
%C A254351 log(3)/log(2) = 1.5849625... (see A020857) is an irrational number. The fractions (2/1, 3/2, 5/3, 8/5, 11/7, 19/12, 46/29, 65/41, 84/53, 317/200, 401/253, 485/306, 569/359, 1054/665, ...) are a sequence of approximations to log(3)/log(2), where each is an improvement on its predecessors.
%C A254351 Numerators are shown here, the respective denominators are A060528 (and can also be found among the terms of A206788), both of which refer to equal divisions of the octave and good approximations to musical harmonics.
%o A254351 (Maxima) x:bfloat(log(3)/log(2)),fpprec:100, errold:2,for denominator:1 thru 10000 do (numerator:round(x*denominator), errnew:abs(x-numerator/denominator), if errnew < errold then (errold:errnew, print(numerator)));
%Y A254351 Cf. A060528 (denominators), A020857, A206788.
%K A254351 nonn,frac
%O A254351 1,1
%A A254351 _K. G. Stier_, Jan 29 2015