A226127 Denominators of signed Egyptian fractions 1/(1+2*a(n)) with sums converging to sqrt(2).

17, 38, 2558, 53508058, 10183965708276283, 833167602683818992272386593114136, 7008824222617646742567474710166940582408242437487752499090108838014

Offset

1,1

Comments

See A226049.

Links

Table of n, a(n) for n=1..7.

Example

The algorithm at A226049, with r = sqrt(2), f(n) = 1/(2n+1), gives
1/3 + 1/5 + 1/7 + ... + 1/(1+2*17) - 1/(1+2*38) + 1/(1+2*2558) - ...
which converges to sqrt(2).  The 17th  partial sum differs from sqrt(2) by less than 10^(-500).

Mathematica

$MaxExtraPrecision = Infinity; z = 9; f[n_] := 1/(2 n + 1); g[n_] := (1/n - 1)/2; r =
Sqrt[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: A293206 A125248 A259489 * A156777 A070142 A070143

Adjacent sequences: A226124 A226125 A226126 * A226128 A226129 A226130

Keyword

nonn

Author

Clark Kimberling, May 27 2013

Status

approved