cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A285481 Smallest integer radius needed such that an n-dimensional ball has a volume greater than or equal to 1.

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%I A285481 #18 Nov 29 2019 22:47:18
%S A285481 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 A285481 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 A285481 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N A285481 Smallest integer radius needed such that an n-dimensional ball has a volume greater than or equal to 1.
%H A285481 Vincenzo Librandi, <a href="/A285481/b285481.txt">Table of n, a(n) for n = 1..1000</a>
%F A285481 a(n) = ceiling((1/(((Pi^(n/2))/(gamma(1+n/2)))))^(1/n)).
%e A285481 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 A285481 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 A285481 Table[Ceiling[(1/(((Pi^(n/2))/(Gamma[1 + n/2]))))^(1/n)], {n, 10^2}] (* _Michael De Vlieger_, Apr 24 2017 *)
%o A285481 (PARI) volume(n, r) = ((Pi^(n/2))/(gamma(1+n/2)))*r^n
%o A285481 a(n) = my(k=1); while(1, if(volume(n, k) >= 1, return(k)); k++)
%Y A285481 Cf. A273264, A285482.
%K A285481 nonn
%O A285481 1,13
%A A285481 _Felix Fröhlich_, Apr 19 2017