OFFSET
1,13
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = ceiling((1/(((Pi^(n/2))/(gamma(1+n/2)))))^(1/n)).
EXAMPLE
a(12) = 1 because a 12-ball of radius 1 has a volume of Pi^6/720 = 1.33526..., which is greater than 1.
a(13) = 2. A 13-ball of radius 1 has a volume of just 0.91..., while a 13-ball of radius 2 has a volume of 7459.87...
MATHEMATICA
Table[Ceiling[(1/(((Pi^(n/2))/(Gamma[1 + n/2]))))^(1/n)], {n, 10^2}] (* Michael De Vlieger, Apr 24 2017 *)
PROG
(PARI) volume(n, r) = ((Pi^(n/2))/(gamma(1+n/2)))*r^n
a(n) = my(k=1); while(1, if(volume(n, k) >= 1, return(k)); k++)
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Apr 19 2017
STATUS
approved