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Search: id:A084973
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| A084973 |
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The maximum departure from the x axis, rounded to the nearest integer, in each cycle of the zeta function for increasingly larger negative values. |
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+0
1
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| 0, 0, 0, 0, 0, 0, -1, 4, -34, 374, -4988, 78674, -1449689, 30854707, -751125115, 20736542367, -644361764772, 22387174696660, -864494448030320, 36906142650945649, -1733457688501062507, 89187472319797248472
(list; graph; listen)
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OFFSET
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-1,8
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COMMENT
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"The zeta function is zero at every negative even number (the trivial zeros), and the successive peaks and troughs now ... get rapidly more and more dramatic as you head west (negative). The last trough I show, which occurs at s = -49.587622654 [6410765611566721701427687663932953145937293907205304283197148592994576700093701122213865946359936710563061421]..., has a depth of about 305,507,128,402,512,981,000,000 (305507128402512978943383.678283221037793184376280971034994413486029678612346873189963110344084662196600996131417814311). You see the difficulty of graphing the zeta function all in one piece." - Derbyshire
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REFERENCES
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John Derbyshire, Prime Obsession, Bernhard Riemann And The Greatest Unsolved Primblem In Mathematics, Joseph Henry Press, Washington, D.C., 2003, page 143.
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EXAMPLE
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a(9) = 34 because between -19 and -21, (at -19.403133257176569932332310530627...), =~ -33.80830359565166465388882152774755514487136542215568...),
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MATHEMATICA
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Table[ Round[ 1/FindMinimum[ 1/Abs[ Zeta[s]], {s, -2t - 1 + {-0.9, +0.9}}, AccuracyGoal -> 50, WorkingPrecision -> 60] [[1]]], {t, 1, 30}]
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CROSSREFS
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Sequence in context: A025572 A093137 A107350 this_sequence A141007 A052630 A071213
Adjacent sequences: A084970 A084971 A084972 this_sequence A084974 A084975 A084976
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KEYWORD
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sign
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), May 23 2003
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