A335931 Decimal expansion of (1/Pi)*arclength on y = sin(x) from (0,0) to (Pi,0).

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

Offset

1,2

Links

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

Formula

Equals A335930 / Pi = (2*sqrt(2)/Pi) * E(1/sqrt(2)), where E(k) is the complete elliptic integral of the second kind. - Amiram Eldar, May 16 2026

Example

(arclength)/(segment length) = 1.21600672342497978031259272328085470564030...

Mathematica

r = NIntegrate[Sqrt[1 + Cos[t]^2]/Pi, {t, 0, Pi}, WorkingPrecision -> 200]
RealDigits[r][[1]]
(* Alternative: *)
RealDigits[2*Sqrt[2]/Pi * EllipticE[1/2], 10, 120][[1]] (* Amiram Eldar, May 16 2026 *)

Prog

(PARI) (2*sqrt(2)/Pi) * ellE(1/sqrt(2)) \\ Amiram Eldar, May 16 2026

Crossrefs

Cf. A335928, A335929, A335930, A335932.

Sequence in context: A110863 A387961 A215219 * A091615 A213279 A175591

Adjacent sequences: A335928 A335929 A335930 * A335932 A335933 A335934

Keyword

nonn,cons

Author

Clark Kimberling, Jul 03 2020

Status

approved