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A345294
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Decimal expansion of Product_{p primes} (1 - 1/p)*(1 + (1 + 1/p)*Sum_{k>=1} 1/(p^k + p^(-k-1))).
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2
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1, 4, 4, 3, 8, 6, 7, 5, 1, 0, 4, 7, 0, 6, 3, 9, 6, 5, 1, 1, 2, 5, 0, 4, 4, 3, 2, 4, 9, 0, 3, 8, 4, 7, 1, 1, 4, 5, 4, 5, 5, 5, 1, 9, 7, 8, 9, 7, 1, 7, 8, 2, 5, 5, 0, 2, 7, 7, 9, 4, 3, 3, 3, 8, 8, 9, 7, 7, 8, 5, 8, 1, 6, 4, 1, 4, 9, 9, 4, 4, 6, 6, 5, 6, 9, 3, 9, 5, 4, 5, 4, 8, 9, 0, 9, 3, 5, 2, 6, 8, 8, 5, 1, 8, 8
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OFFSET
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1,2
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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. 155 (constant C1).
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FORMULA
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Equals lim_{n->infinity} 1/n * Sum_{k=1..n} k^2/A057660(k).
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EXAMPLE
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1.44386751047063965112504432490384711454555197897178255027794333889778581...
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MATHEMATICA
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$MaxExtraPrecision = 1000; m = 500; Do[Clear[f]; f[p_] := (1 - 1/p)*(1 + (1 + 1/p)*Sum[1/(p^j + p^(-j - 1)), {j, 1, k}]); cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x, m + 1]]; Print[f[2]*Exp[N[Sum[Indexed[cc, n]*(PrimeZetaP[n] - 1/2^n), {n, 2, m}], 110]]], {k, 100, 500, 100}]
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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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