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A115456 Decimal expansion of mean perimeter of a quadrilateral inscribed in a square of unit side. 0
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, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..100.

FORMULA

Equals 4 * Integral_{x=0..1, y=0..1} sqrt(x^2 + y^2) = (4/3)*(sqrt(2) + arcsinh(1)).

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

STATUS

approved

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)