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 A114856 Indices n of Gram points g(n) for which (-1)^n Z(g(n)) < 0, where Z(t) is the Riemann-Siegel Z-function. 23
 126, 134, 195, 211, 232, 254, 288, 367, 377, 379, 397, 400, 461, 507, 518, 529, 567, 578, 595, 618, 626, 637, 654, 668, 692, 694, 703, 715, 728, 766, 777, 793, 795, 807, 819, 848, 857, 869, 887, 964, 992, 995, 1016, 1028, 1034, 1043, 1046, 1071, 1086 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS E. C. Titchmarsh, On van der Corput's Method and the zeta-function of Riemann IV, Quarterly Journal of Mathematics os-5 (1934), pp. 98-105. Timothy Trudgian, On the success and failure of Gram's Law and the Rosser Rule, Acta Arithmetica, 2011 | 148 | 3 | 225-256. Eric Weisstein's World of Mathematics, Gram Point Stack Exchange, crow Can we prove B(n)=(1/4)G(n-1)G(n) is an indicator function ... FORMULA Trudgian shows that a(n) = O(n), that is, there exists some k such that a(n) <= kn. - Charles R Greathouse IV, Aug 29 2012 Let g(n)=2*Pi*exp(1+LambertW((1/8)*(8*n+1)/exp(1))) and G(n)=Z(g(n))/|Z(g(n))+Z(g(n+1))/|Z(g(n+1)) and B(n)=(1/4)*G(n-1)*G(n) then B(n)=1 when n is a Bad gram point and B(n)=0 when n is a good Gram point. - Stephen Crowley, Aug 23 2018 EXAMPLE E.g. (-1)^126 Z(g(126)) = -0.0276294988571999... [David Baugh, Apr 02 2008] MATHEMATICA g[n_] := (g0 /. FindRoot[ RiemannSiegelTheta[g0] == Pi*n, {g0, 2*Pi*Exp[1 + ProductLog[(8*n + 1)/(8*E)]]}, WorkingPrecision -> 16]); Reap[For[n = 1, n < 1100, n++, If[(-1)^n*RiemannSiegelZ[g[n]] < 0, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 17 2012, after Eric W. Weisstein *) CROSSREFS Cf. A114857, A114858, A216700. Sequence in context: A308534 A045167 A216063 * A326891 A165019 A025388 Adjacent sequences:  A114853 A114854 A114855 * A114857 A114858 A114859 KEYWORD nonn AUTHOR Eric W. Weisstein, Jan 02 2006 EXTENSIONS Definition corrected by David Baugh, Apr 02 2008 STATUS approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)