A115456 Decimal expansion of mean perimeter of a quadrilateral inscribed in a square of unit side.

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

Offset

1,1

Links

Table of n, a(n) for n=1..103.

Formula

Equals 4 * Integral_{x=0..1, y=0..1} sqrt(x^2 + y^2).

Equals (4/3)*(sqrt(2)+log(sqrt(2)+1)) = (4/3)*(sqrt(2)+arcsinh(1)).

Example

3.0607828658568507653790640655859871834637762715181...

Mathematica

RealDigits[N[(4/3)*(Sqrt[2] + ArcSinh[1]), 100]][[1]]

Prog

(PARI) (sqrt(2)+asinh(1))*4/3 \\ Charles R Greathouse IV, Jul 13 2015

Crossrefs

Sequence in context: A201567 A161829 A290705 * A328788 A007386 A007385

Adjacent sequences: A115453 A115454 A115455 * A115457 A115458 A115459

Keyword

cons,nonn

Author

Zak Seidov, May 07 2007

Extensions

Typo in Mathematica program fixed by Zak Seidov, Nov 19 2011

a(100) corrected by Georg Fischer, Jul 16 2021

Status

approved