A112931 Numerator of rational values arising in an asymptotic formula for 1/(zeta(s)-1) as s-->infinity.

2, 4, 1, 8, 4, 2, 16, 4, 8, 4, 2, 32, 8, 4, 16, 8, 4, 8, 2, 4, 64, 16, 8, 32, 4, 8, 2, 16, 4, 8, 16, 4, 2, 8, 128, 4, 32, 8, 16, 4, 64, 8, 2, 16, 4, 8, 32, 8, 4, 16, 2, 32, 4, 16, 8, 8, 4, 16

Offset

0,1

Links

Table of n, a(n) for n=0..57.

Andrei Vieru, Euler constant as a renormalized value of Riemann zeta function at its pole. Rationals related to Dirichlet L-functions, arXiv:1306.0496 [math.GM], 2015.

Example

1/(zeta(s)-1)=2^s-(4/3)^s-1+(8/9)^s-(4/5)^s+(2/3)^s-(16/27)^s-(4/7)^s+2*(8/15)^s-2*(4/9)^s+(2/5)^s+(32/81)^s+2*(8/21)^s-(4/11)^s-3*(16/45)^s+o((16/45)^x) and here sequence consists of numerators of 2/1,4/3,1/1,8/9,4/5,...

Mathematica

nmax = 20; lz = ConstantArray[0, nmax]; ax = 0; Do[le = Exp[Limit[Log[Abs[(1/(Zeta[x] - 1) - ax)]]/x, x -> Infinity]]; ls = Limit[(1/(Zeta[x] - 1) - ax)/le^x, x -> Infinity]; ax = ax + ls*le^x; lz[[j]] = le; , {j, 1, nmax}]; Numerator[lz] (* Vaclav Kotesovec, Aug 11 2019 *)

Crossrefs

Cf. A112932, A112933.

Sequence in context: A065278 A182896 A207605 * A121685 A125810 A226504

Adjacent sequences: A112928 A112929 A112930 * A112932 A112933 A112934

Keyword

frac,more,nonn

Author

Benoit Cloitre, Oct 06 2005

Extensions

a(15)-a(33) computed by Andrei Vieru, added by Vaclav Kotesovec, Aug 11 2019

Terms a(34) and beyond from Vaclav Kotesovec, Aug 11 2019

Status

approved