A138285 Decimal expansion of the imaginary part of z0, the smallest second-quadrant solution of z = Cos(z).

1, 8, 0, 9, 3, 6, 1, 3, 4, 1, 2, 9, 5, 7, 0, 3, 3, 1, 9, 0, 1, 6, 2, 7, 6, 1, 0, 0, 1, 9, 4, 0, 1, 1, 3, 2, 5, 6, 0, 0, 0, 7, 6, 2, 2, 4, 4, 0, 5, 3, 8, 5, 5, 8, 8, 2, 4, 4, 6, 6, 5, 4, 6, 2, 4, 8, 3, 7, 9, 0, 4, 3, 8, 3, 7, 3, 5, 7, 3, 2, 5, 4, 2, 8, 6, 7, 4, 8, 6, 5, 8, 9, 1, 4, 1, 1, 1, 7, 0, 3, 0, 8, 2, 4, 4

Offset

1,2

Comments

z0 is a repelling fixed point of Cos(z). The only fixed point on the real axis is 0.73908... (A003957), which is an attracting fixed point.

Links

Table of n, a(n) for n=1..105.

Example

1.809361341295703319016276...

Mathematica

z0 = FindRoot[{Re[Cos[x+I*y]]==x, Im[Cos[x+I*y]]==y}, {{x, -2}, {y, 2}}, WorkingPrecision->150]; RealDigits[z0[[2, 2]]]

Crossrefs

Cf. A138284 (real part).

Sequence in context: A243456 A246772 A198820 * A085291 A109219 A199506

Adjacent sequences: A138282 A138283 A138284 * A138286 A138287 A138288

Keyword

cons,nonn

Author

T. D. Noe, Mar 12 2008

Status

approved