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

1,1

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.

Links

Table of n, a(n) for n=1..39.

Prog

(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)));

Crossrefs

Cf. A060528 (denominators), A020857, A206788.

Sequence in context: A006258 A177967 A265741 * A346116 A262841 A332070

Adjacent sequences: A254348 A254349 A254350 * A254352 A254353 A254354

Keyword

nonn,frac

Author

K. G. Stier, Jan 29 2015

Status

approved