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Number of terms (excluding the first) of A002211 for which the geometric mean produces progressively better approximations to Khinchin's constant (itself).
3

%I #39 Jul 16 2024 15:57:43

%S 1,2,3,15,23,26,81,104,109,111,120,127,135,136,141,142,144,145,146,

%T 147,148,5920,5943,8381,8401,89953,91368,267848,353014

%N Number of terms (excluding the first) of A002211 for which the geometric mean produces progressively better approximations to Khinchin's constant (itself).

%C a(30) > 969679. - _Hans Havermann_, Jul 14 2024

%H Hans Havermann, <a href="http://chesswanks.com/pxp/cfk.html">Simple Continued Fraction Expansion of Khinchin's Constant</a>.

%H Marek Wolf, <a href="http://arxiv.org/abs/1112.2412">Computer experiments with Mersenne primes</a>, arXiv preprint arXiv:1112.2412 [math.NT], 2011.

%t cf=Rest[ContinuedFraction[Khinchin,200]];r=2;p=N[1,50];Do[p=p*cf[[i]];m=Abs[p^(1/i)-Khinchin];If[m<r,Print[i];r=m],{i,Length[cf]}] (* _Hans Havermann_, Jul 16 2024 *)

%Y Cf. A002211, A209600.

%K nice,nonn,more

%O 1,2

%A _Hans Havermann_

%E a(28)-a(29) from _Hans Havermann_, Jul 14 2024