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A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2. 19
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 10:27 EDT 2021. Contains 346359 sequences. (Running on oeis4.)