A380601 Decimal expansion of the asymptotic mean of the ratio A322483(k)/A000005(k).
8, 5, 9, 8, 0, 6, 7, 7, 9, 3, 3, 0, 3, 4, 3, 6, 3, 3, 1, 1, 2, 4, 4, 7, 6, 7, 5, 9, 4, 9, 4, 1, 8, 3, 2, 4, 6, 6, 5, 1, 5, 8, 0, 9, 5, 5, 1, 3, 8, 5, 6, 6, 1, 1, 2, 7, 7, 1, 5, 4, 6, 4, 8, 9, 4, 9, 1, 3, 4, 3, 3, 0, 8, 5, 8, 7, 6, 9, 4, 9, 7, 3, 4, 2, 3, 7, 6, 4, 8, 4, 8, 5, 9, 3, 5, 3, 5, 2, 4, 5, 4, 4, 8, 4, 5
Offset: 0
Examples
0.85980677933034363311244767594941832466515809551385...
Crossrefs
Programs
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Mathematica
$MaxExtraPrecision = 1000; m = 1000; f[x_] := (2*x + 3*(x-1)*Log[1 - x] + (x-1)*Log[1+x])/(4*x); c = Rest[CoefficientList[Series[Log[f[x]], {x, 0, m}], x]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k], {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]] -
PARI
default(realprecision, 120); default(parisize, 30000000); my(m = 1024, x = 'x + O('x^m), v); v = Vec((2*x + 3*(x-1)*log(1-x) + (x-1)*log(1+x))/(4*x)); prodeulerrat(sum(i=1, #v, v[i]/p^(i-1)))