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 A335564 #11 Feb 16 2025 08:34:00
%S A335564 1,1,1,0,9,7,4,3,8,8,0,8,4,6,9,1,7,4,4,9,0,0,8,8,7,3,5,8,4,9,3,6,5,7,
%T A335564 9,4,4,6,6,1,8,0,0,2,8,4,2,1,0,1,4,4,8,2,8,5,9,7,7,4,1,6,6,2,3,2,0,5,
%U A335564 2,4,2,5,1,6,6,0,1,6,8,4,3,5,4,3,8,1,8
%N A335564 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 A335564 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 A335564 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 A335564 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DottieNumber.html">Dottie Number</a>.
%H A335564 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dottie_number">Dottie number</a>.
%e A335564 1.11097438808469174490088735849365794466180028421014...
%t A335564 z = {x, y} /. FindRoot[{x == Cos[x]*Cosh[y], y == Sin[x]*Sinh[y]}, {{x, 1}, {y, 1}}, WorkingPrecision -> 100]; RealDigits[z[[2]], 10, 90][[1]]
%Y A335564 Cf. A003957, A335563 (the real part), A335565, A335566.
%K A335564 nonn,cons
%O A335564 1,5
%A A335564 _Amiram Eldar_, Jun 14 2020