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

1,13

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

Cf. A273264, A285482.

Sequence in context: A211670 A036452 A356852 * A282622 A102572 A098391

Adjacent sequences: A285478 A285479 A285480 * A285482 A285483 A285484

Keyword

nonn

Author

Felix Fröhlich, Apr 19 2017

Status

approved