A335563 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.

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, 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, 2, 7, 7, 0, 0, 3, 8, 2, 6, 8, 9, 7, 7, 0, 6, 4, 4, 3, 8

Offset

0,1

Links

Table of n, a(n) for n=0..86.

T. H. Miller, On the numerical values of the roots of the equation cos x = x, Proc. Edinburgh Math. Soc., Vol. 9 (1890), pp. 80-83.

T. Hugh Miller, On the imaginary roots of cos x = x, Proc. Edinburgh Math. Soc., Vol. 21 (1902), pp. 160-162 (the last 3 pages of the pdf file).

Eric Weisstein's World of Mathematics, Dottie Number.

Wikipedia, Dottie number.

Example

0.96226600633306068948508092593102537827547141928666...

Mathematica

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]]

Crossrefs

Cf. A003957, A335564 (the imaginary part), A335565, A335566.

Sequence in context: A269444 A199431 A154899 * A011219 A202543 A188528

Adjacent sequences: A335560 A335561 A335562 * A335564 A335565 A335566

Keyword

nonn,cons

Author

Amiram Eldar, Jun 14 2020

Status

approved