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 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. 2

%I #12 Feb 15 2015 00:49:47

%S 1,6,7,8,28,85,113,198,267,659,1014,10224,13451,537766,925036,1693817,

%T 1803181,2053555,11518526,41877989,66797547,90328940,105345415,

%U 343594795,654075889,934979323,1061368874

%N 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 Inspired by A067561.

%e k c=Pi*k^2 round(c) c-round(c) e=abs(c-round(c))

%e 1 3.14159... 3 0.14159... 0.14159...

%e 2 12.56637... 13 -0.43362... 0.43362...

%e 3 28.27433... 28 0.27433... 0.27433...

%e 4 50.26548... 50 0.26548... 0.26548...

%e 5 78.53981... 79 -0.46018... 0.46018...

%e 6 113.09733... 113 0.09733... 0.09733...

%e 7 153.93804... 154 -0.06195... 0.06195...

%e ...

%e a(1) = 1.

%e 2, 3, 4 and 5 are not in the sequence, because their absolute errors e are greater than that of a(1).

%e 6 is in the sequence, because its absolute error e is less than that of a(1), therefore a(2) = 6.

%e 7 is in the sequence, because its absolute error e is less than that of a(2), therefore a(3) = 7.

%e ...

%o (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 Cf. A067561.

%K nonn

%O 1,2

%A _Kival Ngaokrajang_, Feb 06 2015

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Last modified May 20 01:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)