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A271855
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Decimal expansion of -x_1 such that the Riemann function zeta(x) has at real x_1<0 its first local extremum.
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2
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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x_1 = -2.7172628292045741015705806616765284124247518539174926559440...
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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