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A226050 Denominators of signed Egyptian fractions with sums converging to e. 2
9, 9, 2354, 8114635, 95238369598066, 10137142998831712366552473861, 299020940111770751476683910911849997367708901463842358682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Using the algorithm defined at A226049 with r = e and f(n) = 1/n gives

r = sum{1/k, k=1..9} - 1/9 + 1/2354 - 1/8114635 + ...

r = sum{1/k, k=1..8} + 1/2354 - 1/81154635 + ...; for this second series, the 17th partial sum differs from the e by less than 10^(-900).  For a guide to related sequences, see A226049.

LINKS

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

EXAMPLE

1 + 1/2 + ... + 1/8 < e < 1 + 1/2 + ... + 1/8 + 1/9, so a(1) = 9.

1 + 1/2 + ... + 1/9 - 1/9 < e, so a(2) = 9.

1 + 1/2 + ... + 1/9 - 1/9 + 1/2354 > e, so a(3) = 2354.

MATHEMATICA

$MaxExtraPrecision = Infinity;

nn = 10; f[n_] := 1/n; r = E; 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: A309316 A124116 A213154 * A058200 A067450 A220450

Adjacent sequences:  A226047 A226048 A226049 * A226051 A226052 A226053

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 24 2013

STATUS

approved

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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)