A333204 Decimal expansion of arclength from (0,0) to (1,1) on y = x^4.

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

Offset

1,2

Links

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

Formula

arclength = 2F1(-1/2;1/6;7/6;-16), where 2F1 is the hypergeometric function.

Example

arclength = 1.60022942767220583728997791564995...

Mathematica

s = Integrate[Sqrt[1 + 16 x^6], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

Crossrefs

Cf. A333202, A333203.

Sequence in context: A222118 A267333 A337885 * A186978 A228532 A019956

Adjacent sequences: A333201 A333202 A333203 * A333205 A333206 A333207

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 12 2020

Status

approved