A277682 Decimal expansion of the imaginary part of the fixed point of exp(z) in C congruent with the branch K=1 of log(z)+2*Pi*K*i.

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

Offset

1,1

Comments

Imaginary part of the complex constant z_3 whose real part is in A277681 (see the latter entry for more information).

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Stanislav Sykora, Fixed points of the mappings exp(z) and -exp(z) in C, 2016.

Formula

Let z_3 = A277681+i*A277682. Then z_3 = exp(z_3) = log(z_3)+2*Pi*i = -W_-2(-1).

Example

7.588631178472512622568923954107584383013473671992856360409437...

Mathematica

RealDigits[Im[ProductLog[1, -1]], 10, 105][[1]] (* Jean-François Alcover, Nov 12 2016 *)

Prog

(PARI) default(realprecision, 2050); eps=5.0*10^(default(realprecision))
M(z, K)=log(z)+2*Pi*K*I; \\ the convergent mapping (any K)
K=1; z=1+I; zlast=z;
while(1, z=M(z, K); if(abs(z-zlast)<eps, break); zlast=z);
imag(z)

Crossrefs

Fixed points of +exp(z): z_1: A059526, A059527, A238274, and z_3: A277681 (real part), A277683 (modulus).

Fixed points of -exp(z): z_0: A030178, and z_2: A276759, A276760, A276761.

Sequence in context: A242623 A081815 A115372 * A335864 A199961 A195059

Adjacent sequences: A277679 A277680 A277681 * A277683 A277684 A277685

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 12 2016

Status

approved