OFFSET
0,1
COMMENTS
Real part of all nontrivial zeros of the Riemann zeta function (assuming the Riemann hypothesis to be true). - Alonso del Arte, Jul 02 2011
Radius of a sphere with surface area Pi. - Omar E. Pol, Aug 09 2012
Radius of the midsphere (tangent to the edges) in a regular octahedron with unit edges. Also radius of the inscribed sphere (tangent to faces) in a cube with unit edges. - Stanislav Sykora, Mar 27 2014
Construct a rectangle of maximal area inside an arbitrary triangle. The ratio of the rectangle's area to the triangle's area is 1/2. - Rick L. Shepherd, Jul 30 2014
LINKS
Michael Penn, A creative approach to a scary looking integral., YouTube video, 2020.
Michael Penn, I really like this sum!, YouTube video, 2021.
Wikipedia, Riemann zeta function
Wikipedia, Platonic solid
Index entries for linear recurrences with constant coefficients, signature (1).
FORMULA
Equals Sum_{k>=1} (1/3^k). Hence 1/2 = 0.1111111111111... in base 3.
Cosine of 60 degrees, i.e., cos(Pi/3).
-zeta(0), zeta being the Riemann function. - Stanislav Sykora, Mar 27 2014
a(0) = 5; a(n) = 0, n > 0. - Wesley Ivan Hurt, Mar 27 2014
a(n) = 5 * floor(1/(n + 1)). - Wesley Ivan Hurt, Mar 27 2014
EXAMPLE
1/2 = 0.50000000000000...
MAPLE
Digits:=100; evalf(1/2); # Wesley Ivan Hurt, Mar 27 2014
MATHEMATICA
RealDigits[1/2, 10, 128][[1]] (* Alonso del Arte, Dec 13 2013 *)
LinearRecurrence[{1}, {5, 0}, 99] (* Ray Chandler, Jul 15 2015 *)
PROG
(PARI) { default(realprecision); x=1/2*10; for(n=1, 100, d=floor(x); x=(x-d)*10; print1(d, ", ")) } \\ Felix Fröhlich, Jul 24 2014
(PARI) a(n) = 5*(n==0); \\ Michel Marcus, Jul 25 2014
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved