A226058 Denominators of signed Egyptian fractions with sums converging to the Euler-Mascheroni constant.

1, 2, 12, 163, 57800, 6910401969, 69047272940549306735, 9431570193753590001558014495854550084583

Offset

1,2

Comments

Using the algorithm defined at A226049 with r = Euler-Mascheroni constant (0.577216...) and f(n) gives r = 1 - 1/2 + 1/12 - 1/163 + 1/57800 + ..., of which the 12th partial sum differs from the r by less than 10^(-1900). For a guide to related sequences, see A226049.

Links

Clark Kimberling, Table of n, a(n) for n = 1..11

Example

Let r = Euler-Mascheroni constant.  Then
r < 1 , so a(1) = 1.
1 - 1/2 < r, so a(2) = 2.
1 - 1/2 + 1/12 > r, so a(3) = 12.

Mathematica

$MaxExtraPrecision = Infinity;
nn = 12; f[n_] := 1/n; r = EulerGamma; s = 0; b[1] = NestWhile[# + 1 &, 1, ! (s += f[#]) > r &]; u[1] = Sum[f[n], {n, 1, b[1]}]; c[1] = Floor[1/(u[1] - r)]; v[1] = u[1] - 1/c[1]; n = 1; While[n < nn/2, n++; b[n] = Floor[1/(r - v[n - 1])]; u[n] = v[n - 1] + 1/b[n]; c[n] = Floor[1/(u[n] - r)]; v[n] = u[n] - 1/c[n]]; a = Riffle[Table[b[i], {i, 1, nn/2}], Table[c[i], {i, 1, nn/2}]]

Crossrefs

Cf. A226049.

Sequence in context: A012328 A302688 A201007 * A120958 A030163 A368981

Adjacent sequences: A226055 A226056 A226057 * A226059 A226060 A226061

Keyword

nonn

Author

Clark Kimberling, May 24 2013

Status

approved