A332629 Decimal expansion of arclength between (0,1) and (1,e) on y = e^x.

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

Offset

1,1

Links

Table of n, a(n) for n=1..85.

Formula

arclength = sqrt(1 + e^2) - sqrt(2) + arctanh(sqrt(2)) - arctanh(sqrt(1+e^2)).

Example

arclength = 2.003497111627352478569902752420239130821142795232094...

Mathematica

s = Integrate[Sqrt[1 + E^(2 x)], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Crossrefs

Cf. A333202, A332630, A332631.

Sequence in context: A261319 A230414 A053653 * A262174 A064146 A361100

Adjacent sequences: A332626 A332627 A332628 * A332630 A332631 A332632

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 12 2020

Status

approved