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A019707 Decimal expansion of sqrt(Pi)/5. 7
3, 5, 4, 4, 9, 0, 7, 7, 0, 1, 8, 1, 1, 0, 3, 2, 0, 5, 4, 5, 9, 6, 3, 3, 4, 9, 6, 6, 6, 8, 2, 2, 9, 0, 3, 6, 5, 5, 9, 5, 0, 9, 8, 9, 1, 2, 2, 4, 4, 7, 7, 4, 2, 5, 6, 4, 2, 7, 6, 1, 5, 5, 7, 9, 7, 0, 5, 8, 2, 2, 5, 6, 9, 1, 8, 2, 0, 6, 4, 3, 6, 2, 7, 4, 9, 9, 0, 1, 3, 1, 3, 4, 7, 7, 0, 8, 9, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
With offset 1 this is the decimal expansion of 2*sqrt(Pi) = 3.544907..., which is the smallest possible perimeter index eta=P/sqrt(A) of all figures (not necessarily connected) in the Euclidean plane with a continuous boundary of length P (perimeter) enclosing a finite area A. The smallest value is attained only by a Euclidean planar disk. For example, eta=4 for squares, eta=2(sqrt(a/b)+sqrt(b/a))>=4 for aXb rectangles, and eta=4.559014... (A268604) for equilateral triangles. - Stanislav Sykora, Feb 08 2016
LINKS
FORMULA
sqrt(Pi)/5 = sqrt(4 * Pi)/10.
Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. - Lee A. Newberg, Mar 05 2024
EXAMPLE
0.3544907701811...= 0.2*A002161.
MATHEMATICA
RealDigits[Sqrt[Pi]/5, 10, 100][[1]] (* Alonso del Arte, Jun 10 2012 *)
PROG
(PARI) sqrt(Pi)/5 \\ Charles R Greathouse IV, Sep 28 2022
CROSSREFS
Sequence in context: A086181 A000655 A130532 * A197825 A077861 A272647
KEYWORD
nonn,easy,cons
AUTHOR
STATUS
approved

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Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)