cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Views

Author

Felix Fröhlich, Jan 07 2018

Keywords

Comments

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

Examples

			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...

Links

Crossrefs

Cf. A066645, A135973, A254714, A297840.

Programs

  • 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++)

Extensions

a(15)-a(19) from Jon E. Schoenfield, Jan 07 2018
a(20) from David Consiglio, Jr., Mar 14 2023

A297840 Numbers k > 0 that set a new record for the closeness of 4*Pi*k^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

Views

Author

Felix Fröhlich, Jan 07 2018

Keywords

Comments

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

Examples

			          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...

Crossrefs

Cf. A066644, A135971, A254714, A297839.

Programs

  • Mathematica
    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 *)
  • PARI
    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++)

Extensions

a(23)-a(24) from Jon E. Schoenfield, Jan 07 2018
Showing 1-2 of 2 results.

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