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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 (list; constant; graph; refs; listen; history; text; internal format)
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,-2n-2), n = 1, 2, 3, ..., it attains a local extreme (maximum, minimum, maximum, ...). The location x_n of the n-th local extreme does not match the odd integer -2n-1. Rather, x_n > -2n-1 for n = 1 and 2, and x_n < -2n-1 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*n-1.9999999999, 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

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Last modified May 26 03:22 EDT 2017. Contains 287073 sequences.