This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380519 #6 Feb 08 2025 15:26:26
%S A380519 1,0,0,2,5,0,4,7,1,0,5,5,1,4,0,7,1,3,1,3,9,6,8,5,3,7,8,2,8,0,2,2,2,4,
%T A380519 7,5,9,1,9,1,2,2,7,9,4,8,6,1,5,6,5,1,7,8,1,0,0,4,2,1,3,5,7,5,0,8,5,1,
%U A380519 5,1,9,3,5,1,1,9,9,4,6,4,8,3,0,7,7,2
%N A380519 Decimal expansion of least x>1 so that Re(x^rho) has a local maximum, with rho as the first zeta zero.
%C A380519 Re(x^rho) = sqrt(x) * cos(Im(rho) * log(x)), with rho = 1/2 + i * 14.134725... (A058303).
%C A380519 Further local maxima at: (this constant) * exp(2*Pi*k/A058303), with integer k.
%F A380519 Equals exp(arccos(2*t/sqrt(1+4*t^2))/t), with t = Im(rho).
%e A380519 1.00250471055140713139685378280222475919122794861...
%t A380519 RealDigits[x /. FindRoot[D[Sqrt[x] Cos[Im@ZetaZero@1 Log[x]], x], {x, 1}, WorkingPrecision -> 100][[1]]][[1]]
%Y A380519 Cf. A058303, A199499.
%K A380519 nonn,cons
%O A380519 1,4
%A A380519 _Friedjof Tellkamp_, Jan 26 2025