This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355513 #7 Jul 05 2022 10:35:12
%S A355513 2,3,5,8,13,18,31,75,106,137,517,654,791,928,1719,21419,23138,24857,
%T A355513 26576,28295,30014,31733,33452,35171,36890,38609,40328,82375,205078,
%U A355513 287453,492531,14078321,14570852,15063383,15555914,16048445,16540976,17033507,17526038,18018569
%N A355513 Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that abs(j/k - q) is a new minimum.
%o A355513 (PARI) a355513(upto) = {my(q=log(2)/log(3), dmin=oo);for (m=1, upto, my(n=round(m*q), qq=n/m, d=abs(qq-q)); if(d<dmin, print1(n+m,", "); dmin=d))};
%o A355513 \\ needs increased precision for larger terms
%o A355513 a355513(10^7)
%Y A355513 Cf. A102525, A355512, A355514, A355515.
%K A355513 nonn
%O A355513 1,1
%A A355513 _Hugo Pfoertner_, Jul 05 2022