A271855 Decimal expansion of -x_1 such that the Riemann function zeta(x) has at real x_1<0 its first local extremum.

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

Offset: 1

Author

Stanislav Sykora, Apr 23 2016

Keywords

• nonn
• cons

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.

Examples

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

Links

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

Crossrefs

Cf. A271856.

Programs

PARI

\\ This function was tested up to n = 11600000:
zetaextreme(n) = {solve(x=-2.0*n,-2.0*n-1.9999999999,zeta'(x))}
a = -zetaextreme(1) \\ Evaluation for this entry