A285481 - OEIS

%I #18 Nov 29 2019 22:47:18

%S 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,

%T 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,

%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N Smallest integer radius needed such that an n-dimensional ball has a volume greater than or equal to 1.

%H Vincenzo Librandi, <a href="/A285481/b285481.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling((1/(((Pi^(n/2))/(gamma(1+n/2)))))^(1/n)).

%e a(12) = 1 because a 12-ball of radius 1 has a volume of Pi^6/720 = 1.33526..., which is greater than 1.

%e 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...

%t Table[Ceiling[(1/(((Pi^(n/2))/(Gamma[1 + n/2]))))^(1/n)], {n, 10^2}] (* _Michael De Vlieger_, Apr 24 2017 *)

%o (PARI) volume(n, r) = ((Pi^(n/2))/(gamma(1+n/2)))*r^n

%o a(n) = my(k=1); while(1, if(volume(n, k) >= 1, return(k)); k++)

%Y Cf. A273264, A285482.

%K nonn

%O 1,13

%A _Felix Fröhlich_, Apr 19 2017