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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)