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%I #10 Jun 14 2020 22:46:53
%S 9,6,2,2,6,6,0,0,6,3,3,3,0,6,0,6,8,9,4,8,5,0,8,0,9,2,5,9,3,1,0,2,5,3,
%T 7,8,2,7,5,4,7,1,4,1,9,2,8,6,6,6,4,7,4,1,2,5,5,2,0,9,5,1,6,3,4,8,1,4,
%U 2,7,7,0,0,3,8,2,6,8,9,7,7,0,6,4,4,3,8
%N Decimal expansion of the real part of the complex root of cos(x + i*y) = x - i*y with least x > 0 and y > 0.
%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DottieNumber.html">Dottie Number</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dottie_number">Dottie number</a>.
%e 0.96226600633306068948508092593102537827547141928666...
%t z = {x, y} /. FindRoot[{x == Cos[x]*Cosh[y], y == Sin[x]*Sinh[y]}, {{x, 1}, {y, 1}}, WorkingPrecision -> 100]; RealDigits[z[[1]], 10, 90][[1]]
%Y Cf. A003957, A335564 (the imaginary part), A335565, A335566.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Jun 14 2020