OFFSET
1,2
COMMENTS
Integer radii such that the volume of the corresponding sphere is closer to an integer than for any smaller integer radius.
LINKS
David Consiglio, Jr., Python Program
Sean A. Irvine, Java program (github)
EXAMPLE
k | (4/3)*Pi*k^3 | Deviation from integer
---------------------------------------------------------------------------
1 | 4.188790204786390... | 0.188790204786390...
3 | 113.097335529232556... | 0.097335529232556...
4 | 268.082573106329023... | 0.082573106329023...
14 | 11494.040321933856861... | 0.040321933856861...
18 | 24429.024474314232222... | 0.024474314232222...
23 | 50965.010421636019109... | 0.010421636019109...
62 | 998305.991926330990581... | 0.008073669009418...
95 | 3591364.001828731970435... | 0.001828731970435...
423 | 317036825.999590816501793... | 0.000409183498206...
5339 | 637482653747.999839504336479... | 0.000160495663520...
12352 | 7894060641354.000003942767448... | 0.000003942767448...
108359 | 5329464512150064.999997849950689... | 0.000000215004931...
129805 | 9161421693208264.000000035388795... | 0.000000035388795...
5334194 | 635762677398025211698.999999995151941... | 0.000000004848058...
PROG
(PARI) closeness(n) = my(v=(4/3)*Pi*n^3); if(round(v) > v, return(round(v)-v), return(v-round(v)))
my(r=1, k=1, c=0); while(1, c=closeness(k); if(c < r, print1(k, ", "); r=c); k++)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Felix Fröhlich, Jan 07 2018
EXTENSIONS
a(15)-a(19) from Jon E. Schoenfield, Jan 07 2018
a(20) from David Consiglio, Jr., Mar 14 2023
STATUS
approved