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 A226129 Denominators of signed Egyptian fractions 1/sqrt(n) with sums converging to 2. 0

%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

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Last modified June 3 04:09 EDT 2023. Contains 363103 sequences. (Running on oeis4.)