A079630 Numbers n such that |real(zeta(1/2 + n*I))| exceeds all previous values, where zeta is the Riemann zeta function.

0, 10, 17, 18, 28, 46, 63, 109, 172, 281, 417, 652, 698, 852, 1269, 1550, 3100, 4478, 6726, 7578, 9654, 9826, 10678, 14304, 30775, 45079, 57552, 74956, 105731, 248917, 289346, 340761, 407722, 440699, 457170, 682764, 795112, 849038, 874546, 1138384

Offset: 1

Author

Robert G. Wilson v, Jan 30 2003

Keywords

• nonn

Comments

If you begin at 1 instead of 0, the sequence begins 1,2,3,4,5,6,7,8,9,10,..., etc.

Examples

			|real(zeta(1/2 + 1616584*I))| ~= 44.1381
		

Links

• Glen Pugh, The Riemann Hypothesis in a Nutshell
• Ed Pegg Jr., The Riemann Hypothesis

Crossrefs

Cf. A002410.

Programs

Mathematica

a = -1; Do[b = Abs[ Re[ N[ Zeta[0.5 + n*I]]]]; If[b > a, Print[n]; a = b], {n, 0, 10^6}]
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 *)