A230767 Continued fraction expansion of Mertens' constant (A077761).

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

Offset: 0

Author

Edward Jiang, Oct 29 2013

Keywords

• nonn
• cofr

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A077761 (decimal expansion).

Programs

Mathematica

$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 *)

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

Extensions

a(19) and onward corrected by Charles R Greathouse IV, May 27 2015

Offset changed by Andrew Howroyd, Aug 08 2024