A066644 -id:A066644 - cp's OEIS frontend

A135973 Ceiling(4/3Pin^3).

0, 5, 34, 114, 269, 524, 905, 1437, 2145, 3054, 4189, 5576, 7239, 9203, 11495, 14138, 17158, 20580, 24430, 28731, 33511, 38793, 44603, 50966, 57906, 65450, 73623, 82448, 91953, 102161, 113098, 124789, 137259, 150533, 164637, 179595, 195433

Offset: 0

Mohammad K. Azarian, Mar 02 2008

Volume of a sphere of radius n, rounded up.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A066643, A066644, A066645, A135039.

Table[Ceiling[4/3*Pi * n^3], {n, 0, 60}] (* Vincenzo Librandi, Feb 19 2013 *)

a(n)=ceil(4/3*Pi*n^3) \\ Charles R Greathouse IV, Oct 10 2013

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

a(n) = A066645(n) + 1 for n > 0.

Definition replaced by Vincenzo Librandi, Feb 19 2013

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

A135971 Ceiling(4Pin^2).

Original entry on oeis.org

13, 51, 114, 202, 315, 453, 616, 805, 1018, 1257, 1521, 1810, 2124, 2464, 2828, 3217, 3632, 4072, 4537, 5027, 5542, 6083, 6648, 7239, 7854, 8495, 9161, 9853, 10569, 11310, 12077, 12868, 13685, 14527, 15394, 16287, 17204, 18146, 19114, 20107

Offset: 1

Mohammad K. Azarian, Mar 02 2008

The original definition was "a(n)=ceiling[surface area of a shpere of radius n]".

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

Cf. A066643, A066644, A066645, A135039.

Table[Ceiling[4 Pi n^2], {n, 1, 50}] (* Vincenzo Librandi, Feb 19 2013 *)

Definition replaced by Bruno Berselli, Feb 19 2013

A297840 Numbers k > 0 that set a new record for the closeness of 4Pik^2 to an integer.

Original entry on oeis.org

1, 2, 3, 4, 14, 99, 507, 5112, 9361, 13451, 90425, 132640, 268883, 462518, 1803181, 1890795, 2053555, 3831113, 4166332, 5759263, 38574916, 45164470, 310321816, 530684437

Offset: 1

Felix Fröhlich, Jan 07 2018

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

			          k |                 4*Pi*k^2              | Deviation from
            |                                       | integer
------------+---------------------------------------+----------------------
          1 |                  12.56637061435917... | 0.43362938564082...
          2 |                  50.26548245743669... | 0.26548245743669...
          3 |                 113.09733552923255... | 0.09733552923255...
          4 |                 201.06192982974676... | 0.06192982974676...
         14 |                2463.00864041439789... | 0.00864041439789...
         99 |              123162.99839133425412... | 0.00160866574587...
        507 |             3230173.00005041104861... | 0.00005041104861...
       5112 |           328391233.00004811902011... | 0.00004811902011...
       9361 |          1101169958.00003281689453... | 0.00003281689453...
      13451 |          2273625908.00000716139558... | 0.00000716139558...
      90425 |        102751199128.99999628277400... | 0.00000371722599...
     132640 |        221084802748.99999692741688... | 0.00000307258311...
     268883 |        908524313282.00000157554683... | 0.00000157554683...
     462518 |       2688234448369.99999894165289... | 0.00000105834710...
    1803181 |      40859072996351.99999911345115... | 0.00000088654884...
    1890795 |      44926103614145.99999944953623... | 0.00000055046376...
    2053555 |      52993492455840.00000053265439... | 0.00000053265439...
    3831113 |     184441985069785.99999958888834... | 0.00000041111165...
    4166332 |     218131111695367.00000020961660... | 0.00000020961660...
    5759263 |     416815333018180.99999995070232... | 0.00000004929767...
   38574916 |   18699062881733779.00000003869142... | 0.00000003869142...
   45164470 |   25633251606933903.00000000438530... | 0.00000000438530...
  310321816 | 1210136834140739074.00000000262227... | 0.00000000262227...
  530684437 | 3539016334684589995.00000000014286... | 0.00000000014286...

Cf. A066644, A135971, A254714, A297839.

mx = 1; k = 1; lst = {}; While[k < 3000000001, a = N[ Pi(2k)^2, 32]; a = N[ Abs[a - Round@ a], 32]; If[a < mx, mx = a; AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jan 11 2018 *)

closeness(n) = my(s=4*Pi*n^2); if(round(s) > s, return(round(s)-s), return(s-round(s)))
my(r=1, k=1, c=0); while(1, c=closeness(k); if(c < r, print1(k, ", "); r=c); k++)

a(23)-a(24) from Jon E. Schoenfield, Jan 07 2018

A261791 The integer part of the surface area of the 4-dimensional sphere of radius n.

Original entry on oeis.org

19, 157, 532, 1263, 2467, 4263, 6770, 10106, 14389, 19739, 26272, 34109, 43367, 54164, 66619, 80851, 96978, 115119, 135391, 157913, 182804, 210183, 240166, 272874, 308425, 346936, 388526, 433315, 481419, 532958

Offset: 1

Ilya Gutkovskiy, Sep 01 2015

nonn

2*Pi^2*n^3 - surface area of the 4-dimensional sphere of radius n.

Eric Weisstein's World of Mathematics, Hypersphere
Eric Weisstein's World of Mathematics, Floor Function
Wikipedia, N-sphere

Cf. A038130, A000578, A164102 (2*Pi^2), A210519, A066644.

Mathematica
```
Table[Floor[2 Pi^2 n^3], {n, 1, 30}]
```

a(n) = floor(2*Pi^2*n^3) \\ Charles R Greathouse IV, Sep 18 2015

a(n) = floor(2*Pi^2*n^3).

a(n) = floor(2*Pi^2*A000578(n)).

cp's OEIS Frontend

A135973 Ceiling(4/3*Pi*n^3).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

Extensions

A135971 Ceiling(4*Pi*n^2).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A297840 Numbers k > 0 that set a new record for the closeness of 4*Pi*k^2 to an integer.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A261791 The integer part of the surface area of the 4-dimensional sphere of radius n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A135973 Ceiling(4/3Pin^3).

A135971 Ceiling(4Pin^2).

A297840 Numbers k > 0 that set a new record for the closeness of 4Pik^2 to an integer.