A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2.

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

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Formula

arclength = (2 sqrt(5) + arcsinh(2))/4.

arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.

Example

Equals 1.478942857544597433827906...

Mathematica

s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Crossrefs

Cf. A333203, A333204, A335996.

Sequence in context: A090383 A179620 A310936 * A082390 A011517 A000934

Adjacent sequences: A333199 A333200 A333201 * A333203 A333204 A333205

Keyword

nonn,cons,easy

Author

Clark Kimberling, May 13 2020

Status

approved