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 A226053 Denominators of signed Egyptian fractions with sums converging to sqrt(1/2). 2
 1, 3, 24, 815, 2263886, 9073564639850, 176228569027146222763928594, 84205747605016031994416006285857418872429042805656089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Using the algorithm defined at A226049 with r = sqrt(1/2) and f(n) = 1/n gives r = 1 + 1/2 + 1/3 - 1/24 + 1/815 + 1/2263886 + ..., of which the 14th partial sum differs from the r by less than 10^(-1700). For a guide to related sequences, see A226049. LINKS Clark Kimberling, Table of n, a(n) for n = 1..12 EXAMPLE Let r = sqrt(1/2). Then 1 + 1/2 < r < 1 + 1/2 + 1/3, so a(1) = 3. 1 + 1/2 + 1/3 -1/24 < r, so a(2) = 24. 1 + 1/2 + 1/3 -1/24 + 1/815 > r, so a(3) = 815. MATHEMATICA \$MaxExtraPrecision = Infinity; nn = 12; f[n_] := 1/n; r = Sqrt[1/2]; 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: A326084 A301525 A277177 * A233894 A075655 A300551 Adjacent sequences: A226050 A226051 A226052 * A226054 A226055 A226056 KEYWORD nonn AUTHOR Clark Kimberling, May 24 2013 STATUS approved

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Last modified May 30 10:33 EDT 2023. Contains 363050 sequences. (Running on oeis4.)