

A271855


Decimal expansion of x_1 such that the Riemann function zeta(x) has at real x_1<0 its first local extremum.


2



2, 7, 1, 7, 2, 6, 2, 8, 2, 9, 2, 0, 4, 5, 7, 4, 1, 0, 1, 5, 7, 0, 5, 8, 0, 6, 6, 1, 6, 7, 6, 5, 2, 8, 4, 1, 2, 4, 2, 4, 7, 5, 1, 8, 5, 3, 9, 1, 7, 4, 9, 2, 6, 5, 5, 9, 4, 4, 0, 7, 2, 7, 5, 9, 7, 2, 9, 0, 3, 9, 8, 3, 2, 6, 1, 3, 9, 3, 0, 8, 7, 8, 2, 7, 6, 7, 1, 2, 1, 1, 4, 4, 2, 6, 1, 6, 8, 9, 1, 9, 8, 4, 5, 3, 6
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OFFSET

1,1


COMMENTS

For real x < 0, zeta(x) undergoes divergent oscillations, passing through zero at every even integer value of x. In each interval (2n,2n2), n = 1, 2, 3, ..., it attains a local extreme (maximum, minimum, maximum, ...). The location x_n of the nth local extreme does not match the odd integer 2n1. Rather, x_n > 2n1 for n = 1 and 2, and x_n < 2n1 for n >= 3. This entry defines the location x_1 of the first maximum. The corresponding value is in A271856.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Riemann Zeta Function


EXAMPLE

x_1 = 2.7172628292045741015705806616765284124247518539174926559440...
zeta(x_1) = A271856.


PROG

(PARI) \\ This function was tested up to n = 11600000:
zetaextreme(n) = {return(solve(x=2.0*n, 2.0*n1.9999999999, zeta'(x)); }
a = zetaextreme(1) \\ Evaluation for this entry


CROSSREFS

Cf. A271856.
Sequence in context: A096381 A215941 A156194 * A021372 A170936 A111714
Adjacent sequences: A271852 A271853 A271854 * A271856 A271857 A271858


KEYWORD

nonn,cons


AUTHOR

Stanislav Sykora, Apr 23 2016


STATUS

approved



