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Number of terms of the fractional part of A030168 for which the geometric mean produces increasingly better approximations to Khinchin's constant.
0

%I #7 Sep 13 2024 20:16:29

%S 1,9,10,12,13,26,48,49,51,65,66,67,1330,1331,1332,1336,1337,1338,1339,

%T 1340,1431,5666,10331,537086,537095,538045,576768,576789

%N Number of terms of the fractional part of A030168 for which the geometric mean produces increasingly better approximations to Khinchin's constant.

%C Next term > 3307254.

%F p = Drop[{A030168}, 1]; q = N[1, 100]; r = p[[1]] + 1; t = {}; Do[q = q*p[[i]]; g = q^(1/i) - Khinchin; If[Abs[g] < r, r = Abs[g]; t = Append[t, i]], {i, 1, Length[p]}]; t

%e The geometric mean of 67 terms (Khinchin + 0.0128639) is not bettered until we calculate the geometric mean of 1330 terms (Khinchin + 0.011153).

%Y Cf. A030168, A048613.

%K nonn

%O 1,2

%A _Hans Havermann_, Feb 13 2001