A276761 - OEIS

%I #13 Oct 06 2020 12:14:19

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

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

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

%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_2 = A276759+i*A276760. See A276759 for more information.

%H Stanislav Sykora, <a href="/A276761/b276761.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 4.636284632786625189544952318034205387044699355677575252963935...

%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_0: A030178, and z_2: A276759 (real part), A276760 (imaginary part).

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

%K nonn,cons

%O 1,1

%A _Stanislav Sykora_, Nov 12 2016