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A230767
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Continued fraction expansion of Mertens' constant (A077761).
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2
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0, 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1, 12, 12, 9, 1, 8, 4, 10, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 8, 1, 4, 2, 1, 6, 1, 1, 1, 1, 1, 2, 5, 1, 3, 4, 6, 5, 1, 4, 1, 23
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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$MaxExtraPrecision = 400; ContinuedFraction[N[EulerGamma + NSum[(MoebiusMu[m]/m)*Log[N[Zeta[m], 120]], {m, 2, 1000}, Method -> "EulerMaclaurin", AccuracyGoal -> 120, NSumTerms -> 1000, PrecisionGoal -> 120, WorkingPrecision -> 120], 71]] (* Michael De Vlieger, May 28 2015, after Jean-François Alcover at A077761 *)
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PROG
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(PARI) a()=my(e=precision(2.>>(32*ceil(default(realprecision)*38539962/371253907)) , 9), t, s=Euler, n=1); while((t=log(zeta(n++))/n)>e, s+=moebius(n)*t); t=contfrac(s+moebius(n)*t); t[1..#t-1] \\ Charles R Greathouse IV, May 27 2015
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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