A380270 Decimal expansion of Integral_{x=1..A070769} li(x) dx (negated), where li(x) is the logarithmic integral.

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

Offset

0,1

Comments

A070769 is Soldner's constant, where li(A070769)=0.

Integral_{x=0..1} li(x) dx = -log(2) then Integral_{x=0..A070769} li(x) dx = A380270 - log(2) = -1.19324951683011591582919049...

Links

Table of n, a(n) for n=0..104.

Example

-0.500102336270170606411958373..

Mathematica

y = x /. FindRoot[LogIntegral[x] == 0, {x, 1.5}, WorkingPrecision -> 200]; yy = -Integrate[LogIntegral[x], {x, 1, y}]; RealDigits[yy, 10, 105][[1]]

Crossrefs

Cf. A069284, A070769, A084945, A091723, A244067, A257817, A257818, A257819, A257820, A257821, A270857.

Sequence in context: A186716 A331039 A171915 * A287703 A316480 A099224

Adjacent sequences: A380267 A380268 A380269 * A380271 A380272 A380273

Keyword

cons,nonn

Author

Artur Jasinski, Jan 18 2025

Status

approved