A335996 - OEIS

A335996

Decimal expansion of the number u such that the arclength on y = x^2 from (0,0) to (u, u^2) is 1.

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

u = 0.763926663317091041161960918884092435074956...

MATHEMATICA

x = x /.FindRoot[1/2 x Sqrt[1 + 4 x^2] + 1/4 ArcSinh[2 x] == 1, {x, 0}, WorkingPrecision -> 200]

RealDigits[x][[1]]

CROSSREFS

Cf. A333202.