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A158241
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Decimal expansion of theta = arctan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)).
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1
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2, 7, 6, 7, 8, 7, 1, 7, 9, 4, 4, 8, 5, 2, 2, 6, 2, 5, 7, 5, 4, 2, 6, 6, 3, 6, 5, 0, 4, 4, 6, 3, 4, 2, 6, 0, 0, 1, 7, 5, 1, 1, 9, 1, 1, 3, 5, 0, 3, 5, 8, 1, 6, 1, 6, 6, 9, 1, 3, 4, 8, 0, 1, 8, 5, 8, 4, 2, 7, 5, 8, 4, 7, 4, 4, 3, 4, 0, 6, 9, 8, 5, 0, 3, 3, 5, 4, 2, 8, 2, 1, 7, 1, 5, 4, 2, 6, 6, 0, 3, 5, 8, 6, 3
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OFFSET
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0,1
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COMMENTS
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This number arose in the Davenport-Heilbronn zeta-function which satisfies a functional equation (like zeta) but does not satisfy RH. Some nontrivial zeros are off the critical line (see reference).
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REFERENCES
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P. Borwein et al., The Riemann Hypothesis, Springer (2009), 136-137.
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LINKS
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EXAMPLE
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0.27678717...
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MATHEMATICA
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RealDigits[ArcTan[(Sqrt[10-2*Sqrt[5]]-2)/(Sqrt[5]-1)], 10, 120][[1]] (* Harvey P. Dale, Mar 03 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Keyword:cons inserted, leading zero and offset adjusted by R. J. Mathar, Jul 15 2010
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STATUS
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approved
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