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A226052 Denominators of signed Egyptian fractions with sums converging to sqrt(2). 4
2, 11, 195, 180120, 120479425978, 27716921130006533867139, 1040296455490146050257045342043017466273633682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Using the algorithm defined at A226049 with r = sqrt(2) and f(n) = 1/n gives r = 1 + 1/2 - 1/11 + 1/195 - 1/180120 + ..., of which the 13th partial sum differs from the r by less than 10^(-2900).  For a guide to related sequences, see A226049.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..12

EXAMPLE

Let r = sqrt(2).  Then

1 < r < 1 + 1/2, so a(1) = 2.

1 + 1/2 -1/11 < r, so a(2) = 11.

1 + 1/2 - 1/11 + 1/195 > r, so a(3) = 195.

MATHEMATICA

$MaxExtraPrecision = Infinity;

nn = 12; f[n_] := 1/n; r = Pi; 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: A007984 A132871 A140314 * A271429 A051663 A188203

Adjacent sequences:  A226049 A226050 A226051 * A226053 A226054 A226055

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 24 2013

STATUS

approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)