A135973 -id:A135973 - cp's OEIS frontend

A066645 a(n) = floor( (4/3)Pin^3 ).

0, 4, 33, 113, 268, 523, 904, 1436, 2144, 3053, 4188, 5575, 7238, 9202, 11494, 14137, 17157, 20579, 24429, 28730, 33510, 38792, 44602, 50965, 57905, 65449, 73622, 82447, 91952, 102160, 113097, 124788, 137258, 150532, 164636, 179594, 195432

Offset: 0

Amarnath Murthy, Dec 29 2001

a(n) = A164086(A000578(n)). [Reinhard Zumkeller, Aug 11 2009]

Volume of a sphere of radius n, rounded down.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A000578, A135973, A164086.

Mathematica
```
Table[ Floor[(4/3)Pi*n^3], {n, 0, 50} ]
```

A066645(n):=floor((4/3)*%pi*n^3)$
makelist(A066645(n),n,1,30); /* Martin Ettl, Nov 03 2012 */

{ for (n=0, 1000, write("b066645.txt", n, " ", floor((4/3)*Pi*n^3)) ) } \\ Harry J. Smith, Mar 16 2010

n=100 # change n for more values
[floor(4/3*pi*r^3) for r in [0..n]] # Tom Edgar, Oct 10 2013

a(n) = floor((4/3)*Pi*n^3).

a(n) = A135973(n) - 1 for n > 0.

More terms from Robert G. Wilson v, Jan 03 2002

0 prepended by T. D. Noe, Oct 10 2013

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

Original entry on oeis.org

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

Offset: 1

Felix Fröhlich, Jan 07 2018

Integer radii such that the volume of the corresponding sphere is closer to an integer than for any smaller integer radius.

			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...

David Consiglio, Jr., Python Program
Sean A. Irvine, Java program (github)

Cf. A066645, A135973, A254714, A297840.

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++)

a(15)-a(19) from Jon E. Schoenfield, Jan 07 2018

a(20) from David Consiglio, Jr., Mar 14 2023

cp's OEIS Frontend

A066645 a(n) = floor( (4/3)Pin^3 ).

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

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Author

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cp's OEIS Frontend

A066645 a(n) = floor( (4/3)*Pi*n^3 ).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Maxima

PARI

Sage

Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

A066645 a(n) = floor( (4/3)Pin^3 ).

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