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A065484
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Decimal expansion of Product_{p prime >= 2} (1 + p/((p-1)^2*(p+1))).
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15
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2, 2, 0, 3, 8, 5, 6, 5, 9, 6, 4, 3, 7, 8, 5, 9, 7, 8, 7, 8, 7, 2, 8, 2, 8, 3, 1, 6, 4, 8, 0, 0, 8, 9, 6, 6, 2, 5, 6, 7, 1, 7, 3, 1, 9, 3, 7, 8, 7, 8, 5, 8, 6, 3, 4, 1, 7, 0, 4, 9, 5, 5, 4, 4, 8, 7, 1, 6, 6, 8, 8, 6, 8, 1, 1, 8, 5, 2, 6, 9, 5, 4, 9, 7, 5, 7, 2, 6, 6, 0, 4, 1, 9, 0, 1, 3, 9, 5, 6
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OFFSET
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1,1
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COMMENTS
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
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FORMULA
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Also defined as: Sum_{m>=1} 1/(m*A000010(m)). See Weisstein link.
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EXAMPLE
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2.203856596437859787872828316480...
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MATHEMATICA
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$MaxExtraPrecision = 500; digits = 99; terms = 500; P[n_] := PrimeZetaP[n];
LR = Join[{0, 0, 0}, LinearRecurrence[{2, -1, -1, 1}, {3, 4, 5, 3}, terms + 10]]; r[n_Integer] := LR[[n]]; (Pi^2/6)*Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10] ] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)
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PROG
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(PARI) prodeulerrat(1 + p/((p-1)^2*(p+1))) \\ Hugo Pfoertner, Jun 02 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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