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A276763 Decimal expansion of the imaginary part of a fixed point of the logarithmic integral li(z) in C. 2
2, 0, 6, 5, 9, 2, 2, 2, 0, 2, 3, 7, 0, 6, 6, 2, 1, 8, 8, 9, 8, 8, 1, 0, 4, 6, 1, 1, 2, 5, 4, 1, 0, 8, 4, 3, 0, 0, 1, 4, 2, 4, 9, 8, 5, 3, 1, 9, 0, 0, 6, 7, 3, 2, 8, 3, 8, 5, 7, 9, 1, 1, 8, 0, 4, 5, 9, 8, 8, 5, 9, 4, 9, 3, 2, 6, 0, 6, 7, 7, 7, 7, 8, 3, 5, 5, 5, 4, 5, 7, 0, 2, 8, 2, 7, 1, 5, 9, 2, 8, 4, 6, 7, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A276762 for the real part, as well as detailed comments and links.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000

EXAMPLE

2.06592220237066218898810461125410843001424985319006732838579118...

MATHEMATICA

RealDigits[Im[z/.FindRoot[LogIntegral[z] == z, {z, 2+I}, WorkingPrecision -> 100]]][[1]] (* Vaclav Kotesovec, Oct 30 2016 *)

PROG

(PARI) \\ z may be t_INT, t_REAL, or t_COMPLEX except 0 or 1

li(z)=

{

  my(sgn=(-1)^if(real(z)<1, imag(z)<0, imag(z)<=0));

  sgn*Pi*I - eint1(-log(z));

}

default(realprecision, 2100); \\ Execution:

Eps_= 4.0*10.0^(-default(realprecision));

z=1+I; zlast=0; \\ Initialize and iterate

for(k=1, 1e6, z=li(z); if(abs(z-zlast)<Eps_, break); zlast=z);

imag(z) \\ Display the result

CROSSREFS

Cf. A276762 (real part), A070769.

Sequence in context: A271170 A111520 A145419 * A142354 A105110 A064696

Adjacent sequences:  A276760 A276761 A276762 * A276764 A276765 A276766

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Oct 28 2016

STATUS

approved

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Last modified June 23 18:12 EDT 2017. Contains 288668 sequences.