This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297840 Numbers k > 0 that set a new record for the closeness of 4*Pi*k^2 to an integer. 1
 1, 2, 3, 4, 14, 99, 507, 5112, 9361, 13451, 90425, 132640, 268883, 462518, 1803181, 1890795, 2053555, 3831113, 4166332, 5759263, 38574916, 45164470, 310321816, 530684437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Integer radii such that the surface area of the corresponding sphere is closer to an integer than for any smaller integer radius. LINKS EXAMPLE 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... 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 *) PROG (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++) CROSSREFS Cf. A066644, A135971, A254714, A297839. Sequence in context: A280924 A295756 A140047 * A102483 A134916 A085100 Adjacent sequences:  A297837 A297838 A297839 * A297841 A297842 A297843 KEYWORD nonn,hard,more AUTHOR Felix FrÃ¶hlich, Jan 07 2018 EXTENSIONS a(23)-a(24) from Jon E. Schoenfield, Jan 07 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 19 01:29 EDT 2019. Contains 322237 sequences. (Running on oeis4.)