cp's OEIS Frontend

A059101 Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant.

%I A059101 #18 Sep 13 2024 20:16:38
%S A059101 1,3,7,8,9,10,11,15,16,17,97,100,103,117,976,32307,32760,32787,60508,
%T A059101 60601,60663,187154,230084,1120375,1146529,2211732,4497058,1434927965,
%U A059101 1434935064,1434935232,1434935281,1471575921,1471636101,1490844937,1491643951,1498931686
%N A059101 Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant.
%C A059101 Next term > 3*10^10. - _Hans Havermann_, Jul 29 2024
%C A059101 The geometric mean of 1498931686 terms is Khinchin + 1.00240496*10^-13.
%H A059101 Hans Havermann, <a href="http://chesswanks.com/pxp/cfpi.html">Simple Continued Fraction for Pi</a>
%F A059101 p = Rest[{A001203}]; 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 A059101 The geometric mean of 17 terms (Khinchin + 0.00752006) is not bettered until we calculate the geometric mean of 97 terms (Khinchin - 0.00326655).
%Y A059101 Cf. A001203, A048613.
%K A059101 nonn
%O A059101 1,2
%A A059101 _Hans Havermann_, Feb 13 2001
%E A059101 a(28)-a(36) from _Hans Havermann_, Dec 27 2012