A277683 Decimal expansion of the modulus of the fixed point of exp(z) in C congruent with the branch K=1 of log(z)+2*Pi*K*i.

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

Offset

1,1

Comments

Modulus of z_3 = A277681 + i*A277682. See A277681 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.

Example

7.863861176094232668842573623487382321468320207779893460294144...

Mathematica

RealDigits[Norm[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);
abs(z)

Crossrefs

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

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

Sequence in context: A004496 A197762 A181624 * A143300 A303985 A242816

Adjacent sequences: A277680 A277681 A277682 * A277684 A277685 A277686

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 12 2016

Status

approved