A226128 Denominators of signed Egyptian fractions 1/(1+2*a(n)) with sums converging to 2.

56, 151, 37675, 162957309354, 96984274430119214824218, 10080078376423662538051091122673282619968956943

Offset

1,1

Comments

See A226049.

Links

Table of n, a(n) for n=1..6.

Example

The algorithm at A226049, with r = 2 and f(n) = 1/(2n+1), gives a sum
1/3 + 1/5 + 1/7 + ... + 1/(1+2*56) - 1/(1+2*151) + 1/(1+2*37675) - ...
that converges to 2.  The 64th  partial sum differs from 2 by less than 10^(-700).

Mathematica

$MaxExtraPrecision = Infinity; z = 9; f[n_] := 1/(2 n + 1); g[n_] := (1/n - 1)/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, A226128.

Sequence in context: A201096 A358540 A358860 * A038850 A220042 A220008

Adjacent sequences: A226125 A226126 A226127 * A226129 A226130 A226131

Keyword

nonn

Author

Clark Kimberling, May 27 2013

Status

approved