A230767 - OEIS

%I #27 Aug 09 2024 01:53:43

%S 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,

%T 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,

%U 2,5,1,3,4,6,5,1,4,1,23

%N Continued fraction expansion of Mertens' constant (A077761).

%H Charles R Greathouse IV, <a href="/A230767/b230767.txt">Table of n, a(n) for n = 0..9999</a>

%t $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 *)

%o (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

%Y Cf. A077761 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _Edward Jiang_, Oct 29 2013

%E a(19) and onward corrected by _Charles R Greathouse IV_, May 27 2015

%E Offset changed by _Andrew Howroyd_, Aug 08 2024