cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A048613 Number of terms (excluding the first) of A002211 for which the geometric mean produces progressively better approximations to Khinchin's constant (itself).

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%I A048613 #39 Jul 16 2024 15:57:43
%S A048613 1,2,3,15,23,26,81,104,109,111,120,127,135,136,141,142,144,145,146,
%T A048613 147,148,5920,5943,8381,8401,89953,91368,267848,353014
%N A048613 Number of terms (excluding the first) of A002211 for which the geometric mean produces progressively better approximations to Khinchin's constant (itself).
%C A048613 a(30) > 969679. - _Hans Havermann_, Jul 14 2024
%H A048613 Hans Havermann, <a href="http://chesswanks.com/pxp/cfk.html">Simple Continued Fraction Expansion of Khinchin's Constant</a>.
%H A048613 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 A048613 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 A048613 Cf. A002211, A209600.
%K A048613 nice,nonn,more
%O A048613 1,2
%A A048613 _Hans Havermann_
%E A048613 a(28)-a(29) from _Hans Havermann_, Jul 14 2024