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A335707
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Decimal expansion of Sum_{primes p} log(p) / (p^2 + p - 1).
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5
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4, 1, 8, 7, 5, 7, 5, 7, 8, 7, 9, 4, 1, 2, 5, 4, 8, 0, 5, 3, 4, 4, 2, 1, 2, 5, 6, 0, 2, 8, 7, 0, 4, 6, 3, 6, 1, 3, 6, 5, 5, 5, 1, 6, 5, 4, 4, 9, 2, 8, 7, 0, 2, 9, 4, 0, 5, 2, 2, 0, 0, 2, 8, 0, 3, 7, 7, 5, 4, 9, 6, 9, 2, 5, 9, 5, 2, 8, 9, 0, 8, 0, 2, 1, 4, 8, 0, 6, 7, 2, 8, 4, 7, 7, 8, 5, 1, 1, 8, 8, 8, 5, 9, 4, 0, 0
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OFFSET
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0,1
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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. 100, p. 169.
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EXAMPLE
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0.41875757879412548053442125602870463613655516544928702940522...
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MATHEMATICA
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ratfun = 1 / (p^2 + p - 1); zetas = 0; ratab = Table[konfun = Simplify[ratfun + c/(p^power - 1)] // Together; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*Zeta'[power]/Zeta[power] /. sol; ratfun = konfun /. sol, {power, 2, 20}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 100]], {m, 2000, 20000, 2000}]
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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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