A138284 Decimal expansion of the negative real part of z0, the smallest second-quadrant solution of z = Cos(z).

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

Offset

1,1

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

2.486885698908560230696957...

Mathematica

z0 = FindRoot[{Re[Cos[x+I*y]]==x, Im[Cos[x+I*y]]==y}, {{x, -2}, {y, 2}}, WorkingPrecision->150]; RealDigits[z0[[1, 2]]]

Crossrefs

Cf. A138285 (imaginary part).

Sequence in context: A319078 A246631 A320153 * A175156 A320152 A352763

Adjacent sequences: A138281 A138282 A138283 * A138285 A138286 A138287

Keyword

cons,nonn

Author

T. D. Noe, Mar 12 2008

Status

approved