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.

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, 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, 2, 4, 2, 5, 1, 6, 6, 0, 1, 6, 8, 4, 3, 5, 4, 3, 8, 1, 8

Offset

1,5

Links

Table of n, a(n) for n=1..87.

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

1.11097438808469174490088735849365794466180028421014...

Mathematica

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]]

Crossrefs

Cf. A003957, A335563 (the real part), A335565, A335566.

Sequence in context: A357105 A011115 A019886 * A154482 A155958 A010546

Adjacent sequences: A335561 A335562 A335563 * A335565 A335566 A335567

Keyword

nonn,cons

Author

Amiram Eldar, Jun 14 2020

Status

approved