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%I #10 Jul 29 2024 11:39:02
%S 0,10,17,18,28,46,63,109,172,281,417,652,698,852,1269,1550,3100,4478,
%T 6726,7578,9654,9826,10678,14304,30775,45079,57552,74956,105731,
%U 248917,289346,340761,407722,440699,457170,682764,795112,849038,874546,1138384
%N Numbers n such that |real(zeta(1/2 + n*I))| exceeds all previous values, where zeta is the Riemann zeta function.
%C If you begin at 1 instead of 0, the sequence begins 1,2,3,4,5,6,7,8,9,10,..., etc.
%H Glen Pugh, <a href="http://web.mala.bc.ca/pughg/RiemannZeta/RiemannZetaLong.html">The Riemann Hypothesis in a Nutshell</a>
%H Ed Pegg Jr., <a href="http://www.mathpuzzle.com/riemann.html">The Riemann Hypothesis</a>
%e |real(zeta(1/2 + 1616584*I))| ~= 44.1381
%t a = -1; Do[b = Abs[ Re[ N[ Zeta[0.5 + n*I]]]]; If[b > a, Print[n]; a = b], {n, 0, 10^6}]
%t DeleteDuplicates[Table[{n,Abs[Re[N[Zeta[1/2+n I]]]]},{n,0,12*10^5}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Jul 29 2024 *)
%Y Cf. A002410.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jan 30 2003