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 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. 6
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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). REFERENCES Stanislav Sykora, Fixed points of the mappings exp(z) and -exp(z) in C, http://www.ebyte.it/library/docs/math16/2016_MATH_Sykora_FixedPointsExp.pdf; DOI: 10.3247/SL6Math16.002, 2016. LINKS Stanislav Sykora, Table of n, a(n) for n = 1..2000 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)

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Last modified December 10 19:01 EST 2018. Contains 318049 sequences. (Running on oeis4.)