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 A226127 Denominators of signed Egyptian fractions 1/(1+2*a(n)) with sums converging to sqrt(2). 0
 17, 38, 2558, 53508058, 10183965708276283, 833167602683818992272386593114136, 7008824222617646742567474710166940582408242437487752499090108838014 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A226049. LINKS EXAMPLE The algorithm at A226049, with r = sqrt(2), f(n) = 1/(2n+1), gives 1/3 + 1/5 + 1/7 + ... + 1/(1+2*17) - 1/(1+2*38) + 1/(1+2*2558) - ... which converges to sqrt(2). The 17th partial sum differs from sqrt(2) by less than 10^(-500). MATHEMATICA \$MaxExtraPrecision = Infinity; z = 9; f[n_] := 1/(2 n + 1); g[n_] := (1/n - 1)/2; r = Sqrt[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. Sequence in context: A293206 A125248 A259489 * A156777 A070142 A070143 Adjacent sequences: A226124 A226125 A226126 * A226128 A226129 A226130 KEYWORD nonn AUTHOR Clark Kimberling, May 27 2013 STATUS approved

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Last modified March 29 11:44 EDT 2023. Contains 361599 sequences. (Running on oeis4.)