%I A059101
%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
%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 > 180000000.
%H A059101 H. 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.
%Y A059101 Sequence in context: A064540 A103560 A011398 this_sequence A091679 A116034 
               A122987
%Y A059101 Adjacent sequences: A059098 A059099 A059100 this_sequence A059102 A059103 
               A059104
%K A059101 cofr,nonn
%O A059101 1,2
%A A059101 Hans Havermann (pxp(AT)rogers.com), Feb 13 2001