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.

1, 13, 63, 148, 267, 420, 608, 829, 1085, 1376, 1700, 2058, 2451, 2878, 3339, 3834, 4363, 4927, 5524, 6156, 6822, 7522, 8257, 9025, 9828, 10665, 11536, 12441, 13380, 14354, 15361, 16403, 17479, 18589, 19733, 20912, 22124, 23371, 24652, 25967, 27316, 28700

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Example

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.

Mathematica

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 *)

Prog

(PARI) volume(n, r) = ((Pi^(n/2))/(gamma(1+n/2)))*r^n
a285481(n) = my(k=1); while(1, if(volume(n, k) >= 1, return(k)); k++)
a(n) = my(k=1); while(1, if(a285481(k) >= n, return(k)); k++)

Crossrefs

Cf. A285481.

Sequence in context: A212108 A213843 A031074 * A175109 A265038 A051878

Adjacent sequences: A285479 A285480 A285481 * A285483 A285484 A285485

Keyword

nonn

Author

Felix Fröhlich, Apr 28 2017

Extensions

a(36)-a(42) from Giovanni Resta, Apr 29 2017

Status

approved