

A112931


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


2



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
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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 Lfunctions, arXiv:1306.0496 [math.GM], 2015.


EXAMPLE

1/(zeta(s)1)=2^s(4/3)^s1+(8/9)^s(4/5)^s+(2/3)^s(16/27)^s(4/7)^s+2*(8/15)^s2*(4/9)^s+(2/5)^s+(32/81)^s+2*(8/21)^s(4/11)^s3*(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



