A277683 - OEIS

%I #14 Oct 06 2020 12:14:46

%S 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,

%T 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,

%U 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

%N 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.

%C Modulus of z_3 = A277681 + i*A277682. See A277681 for more information.

%H Stanislav Sykora, <a href="/A277683/b277683.txt">Table of n, a(n) for n = 1..2000</a>

%H Stanislav Sykora, <a href="https://doi.org/10.3247/SL6Math16.002">Fixed points of the mappings exp(z) and -exp(z) in C</a>, 2016.

%e 7.863861176094232668842573623487382321468320207779893460294144...

%t RealDigits[Norm[ProductLog[1, -1]], 10, 105][[1]] (* _Jean-François Alcover_, Nov 12 2016 *)

%o (PARI) default(realprecision,2050);eps=5.0*10^(default(realprecision))

%o M(z,K)=log(z)+2*Pi*K*I; \\ the convergent mapping (any K)

%o K=1;z=1+I;zlast=z;

%o while(1,z=M(z,K);if(abs(z-zlast)<eps,break);zlast=z);

%o abs(z)

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

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

%K nonn,cons

%O 1,1

%A _Stanislav Sykora_, Nov 12 2016