OFFSET
1,2
COMMENTS
Also, with proper offset, decimal expansion of the magnetic permeability of vacuum in SI units, mu_0 = 4*Pi*10^-7 N A^-2, an assigned metrological constant. [This exact expression for mu_0 was valid until the 2019 SI redefinition. In the New SI, mu_0 is numerically very close to that value but is determined only up to a certain error. - Andrey Zabolotskiy, May 22 2019]
Regarding these, see A003678 for general context notes, references and links. - Stanislav Sykora, Jun 16 2012
With offset 2 this is also the decimal expansion of 4*Pi, the surface area of a sphere whose diameter equals the square root of 4, hence its radius is 1. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Jan 18 2013, Oct 05 2013, Dec 22 2013
4*Pi is also the area of the domain bounded by the witch of Agnesi whose Cartesian equation is y = 8 / (x^2 + 4) and its asymptote. More generally (4*Pi) * a^2 is the area of the domain bounded by the witch of Agnesi whose Cartesian equation is y = (8*a^3) / (x^2 + 4*a^2) and its asymptote (Eric Weisstein's link, formula 6). - Bernard Schott, Jun 28 2023
LINKS
Ivan Panchenko, Table of n, a(n) for n = 1..1000
NIST, magnetic constant mu_0.
Nobelprize.org, The Discovery of Quasicrystals (PDF).
Eric Weisstein's World of Mathematics, Witch of Agnesi.
Wikipedia, Crystallographic Restriction Theorem.
FORMULA
Equals Sum_{k>=1} sin(Pi*k/5)/k. - Amiram Eldar, Aug 12 2020
Equals -zeta(3/2)/(10*zeta(-1/2)). - Mats Granvik, May 28 2022
EXAMPLE
1.2566370614359172953850573533118....
mu_0 = 12.566370614359172953850573533118... 10^-7 N/A^2. - Stanislav Sykora, Jun 16 2012
MAPLE
Digits:=100: evalf(2*Pi/5); # Wesley Ivan Hurt, Jan 07 2017
MATHEMATICA
RealDigits[ 2*Pi/5, 10, 111][[1]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 and modified by Robert G. Wilson v *)
PROG
(PARI) 2*Pi/5 \\ G. C. Greubel, Sep 11 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved