A336003 Decimal expansion of the number u such that the arclength on y = e^x from (0,1) to (u, e^u) is 1.

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

Offset: 0

Author

Clark Kimberling, Jul 06 2020

Keywords

• nonn
• cons

Examples

			u = 0.5897552158402901575359617596...
		

Crossrefs

Cf. A336002.

Programs

Mathematica

u = u /. FindRoot[-Sqrt[2] + Sqrt[1 + E^(2 u)] + ArcTanh[Sqrt[2]] -
    ArcTanh[Sqrt[1 + E^(2 u)]] - 1, {u, 0}, WorkingPrecision -> 100]
RealDigits[u][[1]]