cp's OEIS Frontend

A205326 Decimal expansion of the sum of [0;n,n,n,...]^2 for n=1..infinity.

%I A205326 #14 Mar 31 2018 14:47:47
%S A205326 9,1,5,5,8,7,9,1,9,9,0,1,8,1,9,7,2,5,1,9,9,8,1,6,8,5,3,8,0,3,1,9,0,0,
%T A205326 8,9,7,3,5,3,2,0,4,6,0,1,8,9,6,6,9,0,2,4,1,2,2,7,6,9,5,1,7,0,9,6,2,1,
%U A205326 8,2,7,0,5,5,6,4,6,5,3,3,5,9,7,5,5,3,7
%N A205326 Decimal expansion of the sum of [0;n,n,n,...]^2 for n=1..infinity.
%C A205326 This is the total area of all squares with sides parallel to the axes of the Cartesian coordinate system, the lower left vertex at (n,0) and the upper right vertex on f(x)=1/x for n=1..infinity.
%H A205326 Martin Janecke, <a href="http://prlbr.de/2010/01/edle-reihe/">Edle Reihe</a>
%F A205326 Sum_{n>=1} 1/[n;n,n,...]^2.
%F A205326 Sum_{n>=1} 4/(n + sqrt(n^2 + 4))^2.
%e A205326 0.9155879199018197251998168538031900897353...
%o A205326 (PARI) zeta(2)+sumpos(n=1,4/(n+sqrt(n^2+4))^2-1/n^2) \\ _Charles R Greathouse IV_, Jan 26 2012
%Y A205326 Cf. A013661, A205325, continued fractions A001622, A014176, A098316, A098317, A098318.
%K A205326 cons,nonn
%O A205326 0,1
%A A205326 _Martin Janecke_, Jan 26 2012
%E A205326 a(-5)-a(-86) from _Charles R Greathouse IV_, Jan 26 2012