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

0,2

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A077761 (decimal expansion).

Sequence in context: A010285 A159878 A346562 * A324116 A030757 A004592

Adjacent sequences: A230764 A230765 A230766 * A230768 A230769 A230770

Keyword

nonn,cofr

Author

Edward Jiang, Oct 29 2013

Extensions

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

Offset changed by Andrew Howroyd, Aug 08 2024

Status

approved