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

Author

Artur Jasinski, Jan 18 2025

Keywords

• cons
• nonn

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...

Examples

			-0.500102336270170606411958373..
		

Crossrefs

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

Programs

Mathematica

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