cp's OEIS Frontend

A254714 Numbers k such that the area of a circle of radius k is closer to an integer than the area of any circle whose radius is a smaller positive integer k.

%I A254714 #12 Feb 15 2015 00:49:47
%S A254714 1,6,7,8,28,85,113,198,267,659,1014,10224,13451,537766,925036,1693817,
%T A254714 1803181,2053555,11518526,41877989,66797547,90328940,105345415,
%U A254714 343594795,654075889,934979323,1061368874
%N A254714 Numbers k such that the area of a circle of radius k is closer to an integer than the area of any circle whose radius is a smaller positive integer k.
%C A254714 Inspired by A067561.
%e A254714 k   c=Pi*k^2   round(c)   c-round(c)  e=abs(c-round(c))
%e A254714 1    3.14159...    3      0.14159...     0.14159...
%e A254714 2   12.56637...   13     -0.43362...     0.43362...
%e A254714 3   28.27433...   28      0.27433...     0.27433...
%e A254714 4   50.26548...   50      0.26548...     0.26548...
%e A254714 5   78.53981...   79     -0.46018...     0.46018...
%e A254714 6  113.09733...  113      0.09733...     0.09733...
%e A254714 7  153.93804...  154     -0.06195...     0.06195...
%e A254714 ...
%e A254714 a(1) = 1.
%e A254714 2, 3, 4 and 5 are not in the sequence, because their absolute errors e are greater than that of a(1).
%e A254714 6 is in the sequence, because its absolute error e is less than that of a(1), therefore a(2) = 6.
%e A254714 7 is in the sequence, because its absolute error e is less than that of a(2), therefore a(3) = 7.
%e A254714 ...
%o A254714 (PARI){m=1;for(n=1,10^10,c=Pi*n^2;e=abs(c-round(c));if(e<m,m=e;print1(n,", ")))}
%Y A254714 Cf. A067561.
%K A254714 nonn
%O A254714 1,2
%A A254714 _Kival Ngaokrajang_, Feb 06 2015