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.
%I A297840 #25 Jan 22 2018 08:12:59
%S A297840 1,2,3,4,14,99,507,5112,9361,13451,90425,132640,268883,462518,1803181,
%T A297840 1890795,2053555,3831113,4166332,5759263,38574916,45164470,310321816,
%U A297840 530684437
%N A297840 Numbers k > 0 that set a new record for the closeness of 4*Pi*k^2 to an integer.
%C A297840 Integer radii such that the surface area of the corresponding sphere is closer to an integer than for any smaller integer radius.
%e A297840 k | 4*Pi*k^2 | Deviation from
%e A297840 | | integer
%e A297840 ------------+---------------------------------------+----------------------
%e A297840 1 | 12.56637061435917... | 0.43362938564082...
%e A297840 2 | 50.26548245743669... | 0.26548245743669...
%e A297840 3 | 113.09733552923255... | 0.09733552923255...
%e A297840 4 | 201.06192982974676... | 0.06192982974676...
%e A297840 14 | 2463.00864041439789... | 0.00864041439789...
%e A297840 99 | 123162.99839133425412... | 0.00160866574587...
%e A297840 507 | 3230173.00005041104861... | 0.00005041104861...
%e A297840 5112 | 328391233.00004811902011... | 0.00004811902011...
%e A297840 9361 | 1101169958.00003281689453... | 0.00003281689453...
%e A297840 13451 | 2273625908.00000716139558... | 0.00000716139558...
%e A297840 90425 | 102751199128.99999628277400... | 0.00000371722599...
%e A297840 132640 | 221084802748.99999692741688... | 0.00000307258311...
%e A297840 268883 | 908524313282.00000157554683... | 0.00000157554683...
%e A297840 462518 | 2688234448369.99999894165289... | 0.00000105834710...
%e A297840 1803181 | 40859072996351.99999911345115... | 0.00000088654884...
%e A297840 1890795 | 44926103614145.99999944953623... | 0.00000055046376...
%e A297840 2053555 | 52993492455840.00000053265439... | 0.00000053265439...
%e A297840 3831113 | 184441985069785.99999958888834... | 0.00000041111165...
%e A297840 4166332 | 218131111695367.00000020961660... | 0.00000020961660...
%e A297840 5759263 | 416815333018180.99999995070232... | 0.00000004929767...
%e A297840 38574916 | 18699062881733779.00000003869142... | 0.00000003869142...
%e A297840 45164470 | 25633251606933903.00000000438530... | 0.00000000438530...
%e A297840 310321816 | 1210136834140739074.00000000262227... | 0.00000000262227...
%e A297840 530684437 | 3539016334684589995.00000000014286... | 0.00000000014286...
%t A297840 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 *)
%o A297840 (PARI) closeness(n) = my(s=4*Pi*n^2); if(round(s) > s, return(round(s)-s), return(s-round(s)))
%o A297840 my(r=1, k=1, c=0); while(1, c=closeness(k); if(c < r, print1(k, ", "); r=c); k++)
%Y A297840 Cf. A066644, A135971, A254714, A297839.
%K A297840 nonn,hard,more
%O A297840 1,2
%A A297840 _Felix Fröhlich_, Jan 07 2018
%E A297840 a(23)-a(24) from _Jon E. Schoenfield_, Jan 07 2018