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

3, 12, 56204, 8145588993660690, 12344182040136861080220977755600651263940429857583666

Offset

1,1

Comments

See A226049.

Links

Table of n, a(n) for n=1..5.

Example

The algorithm at A226049, with r = 2 and f(n) = n^(-1/2), gives
1/1 + 1/sqrt(2) + 1/sqrt(3) - 1/sqrt(12) + 1/sqrt(56204) - ... ,
converging to 2.  The 11th partial sum differs from 2 by less than 10^(-19000).

Mathematica

$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}])]];
Table[a[k], {k, 1, z}]

Crossrefs

Cf. A226049.

Sequence in context: A036300 A169815 A239891 * A167368 A318165 A215240

Adjacent sequences: A226126 A226127 A226128 * A226130 A226131 A226132

Keyword

nonn,frac

Author

Clark Kimberling, May 27 2013

Status

approved