A297839 Numbers k > 0 that set a new record for the closeness of (4/3)*Pi*k^3 to an integer.

1, 3, 4, 14, 18, 23, 62, 95, 423, 5339, 12352, 108359, 129805, 5334194, 82007322, 90401717, 199671691, 434184265, 655956850, 44438886071

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

Table of n, a(n) for n=1..20.

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

Cf. A066645, A135973, A254714, A297840.

Sequence in context: A281524 A377732 A299040 * A279938 A280331 A079274

Adjacent sequences: A297836 A297837 A297838 * A297840 A297841 A297842

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