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A226124
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Denominators of signed reciprocal primes with sums converging to 1.
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1
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OFFSET
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1,1
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COMMENTS
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The algorithm at A226049, with r = 1 and f(n) = 1/prime(n), gives the sum 1/2 + 1/3 + 1/5 - 1/29 + 1/863 - 1/107251 + 1/1519341947 - ... = 1, of which the denominators on the left side comprise this sequence.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..14
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EXAMPLE
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1/2 + 1/3 + 1/5 - 1/29 + 1/863 - 1/107251 + 1/1519341947 differs from 1 by less than 10^(-18).
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MATHEMATICA
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p[n_] := Prime[n]; q[x_] := PrimePi[x]; r = 1; u = 1/2 + 1/3 + 1/5; c[1] = q[1/(u - r)]; c[2] = q[1/(r - u + 1/p[c[1]])]; c[3] = q[1/(u - r - 1/p[c[1]] + 1/p[c[2]])]; c[4] = q[1/(r - u + 1/p[c[1]] - 1/p[c[2]] + 1/p[c[3]])]; Union[{2, 3, 5}, Table[p[c[i]], {i, 1, 4}]]
seq={2, 3, 5}; sum=Total@(1/seq); While[Length[seq]<10, p=NextPrime[Abs[1/(sum-1)], -1]; sum+=Sign[1-sum]/p; AppendTo[seq, p]]; seq (* Amiram Eldar, Mar 13 2019 *)
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CROSSREFS
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Cf. A226049.
Sequence in context: A107451 A093490 A073309 * A110389 A083388 A090475
Adjacent sequences: A226121 A226122 A226123 * A226125 A226126 A226127
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, May 27 2013
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EXTENSIONS
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a(8)-a(10) from Amiram Eldar, Mar 13 2019
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STATUS
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approved
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