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.

A285482 Smallest k such that A285481(k) >= n, i.e., lowest d where the smallest integer radius needed for a d-dimensional ball to have a volume >= 1 is at least n.

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%I A285482 #8 Apr 30 2017 23:14:06
%S A285482 1,13,63,148,267,420,608,829,1085,1376,1700,2058,2451,2878,3339,3834,
%T A285482 4363,4927,5524,6156,6822,7522,8257,9025,9828,10665,11536,12441,13380,
%U A285482 14354,15361,16403,17479,18589,19733,20912,22124,23371,24652,25967,27316,28700
%N A285482 Smallest k such that A285481(k) >= n, i.e., lowest d where the smallest integer radius needed for a d-dimensional ball to have a volume >= 1 is at least n.
%e A285482 For n = 3: a 63-ball of radius 2 has a volume of 0.91035..., while a 63-ball of radius 3 has a volume of 112969101106.64166... Since 63 is the least number of dimensions where a ball with unit volume has a radius >= 3, a(3) = 63.
%t A285482 a[1]=1; a[n_]:=a[n] = Block[{k = a[n-1]},  While[Ceiling[(Pi^(-k/2) Gamma[1 + k/2])^(1/k)] < n, k++]; k]; Array[a, 20] (* _Giovanni Resta_, Apr 29 2017 *)
%o A285482 (PARI) volume(n, r) = ((Pi^(n/2))/(gamma(1+n/2)))*r^n
%o A285482 a285481(n) = my(k=1); while(1, if(volume(n, k) >= 1, return(k)); k++)
%o A285482 a(n) = my(k=1); while(1, if(a285481(k) >= n, return(k)); k++)
%Y A285482 Cf. A285481.
%K A285482 nonn
%O A285482 1,2
%A A285482 _Felix Fröhlich_, Apr 28 2017
%E A285482 a(36)-a(42) from _Giovanni Resta_, Apr 29 2017