A112933 Constant terms arising in an asymptotic formula for 1/(zeta(s)-1) as s --> infinity.

1, -1, -1, 1, -1, 1, -1, -1, 2, -2, 1, 1, 2, -1, -3, 1, -1, 3, 1, -3, -1, -3, 2, 4, -1, 2, 1, -3, -1, 2, -4, -3, 1, 7, 1, -1, 4, 1, -3, -2, -5, 2, 1, -6, -3, 2, 6, 2, -1, -3, 1, 5, -1, -1, 7, 2, -3, -13

Offset

0,9

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 gives constant terms before rational powers :1,-1,-1,1,-1,1,-1,-1,2,-2,1,1,2,-1,-3,...

Mathematica

nmax = 20; lz = ConstantArray[0, nmax]; lc = 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; lc[[j]] = ls; , {j, 1, nmax}]; lc (* Vaclav Kotesovec, Aug 11 2019 *)

Crossrefs

Cf. A112931, A112932.

Sequence in context: A130633 A266499 A226621 * A270650 A088427 A255350

Adjacent sequences: A112930 A112931 A112932 * A112934 A112935 A112936

Keyword

more,sign

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