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

2, 3, 5, 8, 11, 19, 46, 65, 84, 317, 401, 485, 569, 1054, 13133, 14187, 15241, 16295, 17349, 18403, 19457, 20511, 21565, 22619, 23673, 24727, 50508, 125743, 176251, 301994, 8632083, 8934077, 9236071, 9538065, 9840059, 10142053, 10444047, 10746041, 11048035

Offset: 1

Author

K. G. Stier, Jan 29 2015

Keywords

• nonn
• frac

Comments

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.

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.

Crossrefs

Cf. A060528 (denominators), A020857, A206788.

Programs

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)));