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A271727
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Decimal expansion of the density of exponentially 2^n-numbers (A138302).
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8
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8, 7, 2, 4, 9, 7, 1, 7, 9, 3, 5, 3, 9, 1, 2, 8, 1, 3, 5, 5, 8, 0, 0, 7, 7, 1, 4, 3, 3, 2, 5, 3, 1, 8, 6, 6, 9, 1, 9, 5, 8, 3, 9, 3, 9, 7, 7, 7, 3, 3, 3, 7, 3, 7, 6, 5, 4, 1, 2, 4, 2, 2, 6, 2, 1, 3, 1, 1, 2, 7, 8, 3, 5, 9, 0, 3, 9, 8, 1, 4, 2, 9, 7, 9, 2, 2, 1, 7, 8, 4, 4, 1, 6, 5, 9, 9, 1, 5
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Product_{prime p} f(1/p), where f(x) = 1-x^3+Sum_{n>=2}(x^(2^n)-x^(1+2^n)).
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EXAMPLE
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0.87249717935391281355800771433253186691958393977733373765412...
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MATHEMATICA
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$MaxExtraPrecision = m = 500; em = 10; f[x_] := Log[1 - x^3 + Sum[x^(2^e) - x^(1 + 2^e), {e, 2, em}]]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 105][[1]] (* Amiram Eldar, Sep 09 2022 *)
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CROSSREFS
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Cf. A271726 (Expansion of log(f(x)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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