login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 12:50 EST 2019. Contains 329958 sequences. (Running on oeis4.)