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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.

A355512 Sum of numerator and denominator in the convergents of the approximation of log(2)/log(3) by a continued fraction.

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%I A355512 #16 Aug 02 2024 11:50:49
%S A355512 2,3,5,13,31,106,137,791,1719,40328,82375,205078,287453,492531,
%T A355512 27376658,27869189,138853414,444429431,583282845,1027712276,
%U A355512 15998966985,17026679261,169239080334,355504839929,1946763279979,13982847799782,15929611079761,29912458879543,135579446597933
%N A355512 Sum of numerator and denominator in the convergents of the approximation of log(2)/log(3) by a continued fraction.
%o A355512 (PARI) a355512(upto) = {my(q=log(2)/log(3), fa=oo); for (denmax=1, upto, my(f=bestappr(q,denmax)); if (fa!=f, print1(numerator(f)+denominator(f),", "); fa=f))};
%o A355512 \\ needs increased precision for larger terms
%o A355512 a355512(10^6)
%o A355512 (PARI) \\ See also A005663 and A005664 for efficient code.
%Y A355512 Cf. A005663, A005664, A102525, A355513, A355515.
%Y A355512 Cf. A355514 for the relation to potential cycle lengths of the 3x+1 problem.
%K A355512 nonn
%O A355512 1,1
%A A355512 _Hugo Pfoertner_, Jul 05 2022