

A285481


Smallest integer radius needed such that an ndimensional ball has a volume greater than or equal to 1.


2



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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET

1,13


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


FORMULA

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


EXAMPLE

a(12) = 1 because a 12ball of radius 1 has a volume of Pi^6/720 = 1.33526..., which is greater than 1.
a(13) = 2. A 13ball of radius 1 has a volume of just 0.91..., while a 13ball of radius 2 has a volume of 7459.87...


MATHEMATICA

Table[Ceiling[(1/(((Pi^(n/2))/(Gamma[1 + n/2]))))^(1/n)], {n, 10^2}] (* Michael De Vlieger, Apr 24 2017 *)


PROG

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


CROSSREFS

Cf. A273264, A285482.
Sequence in context: A255270 A211670 A036452 * A282622 A102572 A098391
Adjacent sequences: A285478 A285479 A285480 * A285482 A285483 A285484


KEYWORD

nonn


AUTHOR

Felix FrÃ¶hlich, Apr 19 2017


STATUS

approved



