A276760 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.

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

Offset

1,1

Comments

Imaginary part of the complex constant z_2 whose real part is in A276759 (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_2 = A276759+i*A276760. Then z_2 = -exp(z_2) = log(-z_2)+2*Pi*i = -W_-1(1).

Example

4.375185153061898385470906564852584291623823114677011864961044...

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_0: A030178, and z_2: A276759 (real part), A276761 (modulus).

Fixed points of +exp(z): z_1: A059526, A059527, A238274, and z_3: A277681, A277682, A277683.

Sequence in context: A046548 A127752 A198874 * A365214 A257876 A093051

Adjacent sequences: A276757 A276758 A276759 * A276761 A276762 A276763

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 12 2016

Status

approved