OFFSET
0,1
LINKS
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
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