%I #5 May 31 2013 18:59:03
%S 3,12,56204,8145588993660690,
%T 12344182040136861080220977755600651263940429857583666
%N Denominators of signed Egyptian fractions 1/sqrt(n) with sums converging to 2.
%C See A226049.
%e The algorithm at A226049, with r = 2 and f(n) = n^(1/2), gives
%e 1/1 + 1/sqrt(2) + 1/sqrt(3)  1/sqrt(12) + 1/sqrt(56204)  ... ,
%e converging to 2. The 11th partial sum differs from 2 by less than 10^(19000).
%t $MaxExtraPrecision = Infinity; z = 10; f[n_] := n^(1/2); g[n_] := 1/n^2; r = 2; s = 0; a[1] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= r &]; p = Sum[f[n], {n, 1, a[1]}]; a[2] = Floor[g[p  r]]; a[n_] := Floor[g[((1)^n) (p  r  Sum[((1)^k) f[a[k]], {k, 2, n  1}])]];
%t Table[a[k], {k, 1, z}]
%Y Cf. A226049.
%K nonn,frac
%O 1,1
%A _Clark Kimberling_, May 27 2013
