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A297839 Numbers k > 0 that set a new record for the closeness of (4/3)*Pi*k^3 to an integer. 2
1, 3, 4, 14, 18, 23, 62, 95, 423, 5339, 12352, 108359, 129805, 5334194, 82007322, 90401717, 199671691, 434184265, 655956850, 44438886071 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A282604 A281524 A299040 * A279938 A280331 A079274
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

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)