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