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Denominators of signed Egyptian fractions 1/(1+2*a(n)) with sums converging to 2.
1

%I #4 May 30 2013 16:58:40

%S 56,151,37675,162957309354,96984274430119214824218,

%T 10080078376423662538051091122673282619968956943

%N Denominators of signed Egyptian fractions 1/(1+2*a(n)) with sums converging to 2.

%C See A226049.

%e The algorithm at A226049, with r = 2 and f(n) = 1/(2n+1), gives a sum

%e 1/3 + 1/5 + 1/7 + ... + 1/(1+2*56) - 1/(1+2*151) + 1/(1+2*37675) - ...

%e that converges to 2. The 64th partial sum differs from 2 by less than 10^(-700).

%t $MaxExtraPrecision = Infinity; z = 9; f[n_] := 1/(2 n + 1); g[n_] := (1/n - 1)/2; r = 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}])]];

%t Table[a[k], {k, 1, z}]

%Y Cf. A226049, A226128.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 27 2013