A285481 Smallest integer radius needed such that an n-dimensional ball has a volume greater than or equal to 1.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
Offset: 1
Keywords
Examples
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...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Table[Ceiling[(1/(((Pi^(n/2))/(Gamma[1 + n/2]))))^(1/n)], {n, 10^2}] (* Michael De Vlieger, Apr 24 2017 *) -
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++)
Formula
a(n) = ceiling((1/(((Pi^(n/2))/(gamma(1+n/2)))))^(1/n)).