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 A335566 #9 Feb 16 2025 08:34:00
%S A335566 2,5,4,4,8,8,5,7,6,6,8,8,5,7,0,9,3,2,6,5,5,5,9,7,0,4,2,5,6,7,3,0,9,9,
%T A335566 7,2,3,5,4,8,2,2,5,8,0,1,6,8,0,8,1,6,1,2,3,1,3,8,4,1,9,1,7,3,3,0,5,3,
%U A335566 3,8,5,7,2,0,0,9,8,1,3,1,8,0,4,5,3,1,7
%N A335566 Decimal expansion of the imaginary part of the complex root of cos(x + i*y) = x + i*y with least x > 0 and y > 0.
%H A335566 Henry E. Fettis, <a href="https://www.jstor.org/stable/2005324">Complex Roots of sin z = az, cos z = az, and cosh z = az</a>, Mathematics of Computation, Vol. 30, No. 135 (1976), pp. 541-545, Table 18, <a href="https://doi.org/10.1090/S0025-5718-1976-0418401-9">alternative link</a> (without the tables).
%H A335566 T. H. Miller, <a href="http://dx.doi.org/10.1017/S0013091500030868">On the numerical values of the roots of the equation cos x = x</a>, Proc. Edinburgh Math. Soc., Vol. 9 (1890), pp. 80-83.
%H A335566 T. Hugh Miller, <a href="https://doi.org/10.1017/S001309150003460X">On the imaginary roots of cos x = x</a>, Proc. Edinburgh Math. Soc., Vol. 21 (1902), pp. 160-162 (the last 3 pages of the pdf file).
%H A335566 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DottieNumber.html">Dottie Number</a>.
%H A335566 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dottie_number">Dottie number</a>.
%e A335566 2.54488576688570932655597042567309972354822580168081...
%t A335566 z = {x, y} /. FindRoot[{x == Cos[x]*Cosh[y], y == -Sin[x]*Sinh[y]}, {{x, 5}, {y, 2}}, WorkingPrecision -> 100]; RealDigits[z[[2]], 10, 90][[1]]
%Y A335566 Cf. A003957, A335563, A335564, A335565 (the real part).
%K A335566 nonn,cons
%O A335566 1,1
%A A335566 _Amiram Eldar_, Jun 14 2020