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Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that q - j/k is a new minimum, i.e., q is approximated from below.

5

`%I #7 Jul 05 2022 10:34:55
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`%S 1,3,8,13,44,75,106,243,380,517,654,791,2510,4229,5948,7667,9386,
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`%T 11105,12824,14543,16262,17981,19700,21419,23138,24857,26576,28295,
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`%U 30014,31733,33452,35171,36890,38609,40328,122703,205078,492531,27869189,166722603,305576017
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`%N Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that q - j/k is a new minimum, i.e., q is approximated from below.
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`%o (PARI) a355514(upto) = {my(q=log(2)/log(3), dmin=oo);for (m=1, upto, my(n=floor(m*q), qq=n/m, d=q-qq); if (d<dmin, print1(n+m,", "); dmin=d))};
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`%o \\ needs increased precision for larger terms
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`%o a355514(10^7)
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`%Y Cf. A102525, A355512, A355513, A355515.
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`%Y Terms are candidates for being in A355240, which shares 3, 8, 13, 44, 75.
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`%K nonn
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`%O 1,2
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`%A _Hugo Pfoertner_, Jul 05 2022
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