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.
1, 6, 7, 8, 28, 85, 113, 198, 267, 659, 1014, 10224, 13451, 537766, 925036, 1693817, 1803181, 2053555, 11518526, 41877989, 66797547, 90328940, 105345415, 343594795, 654075889, 934979323, 1061368874
Offset: 1
Keywords
Examples
k c=Pi*k^2 round(c) c-round(c) e=abs(c-round(c)) 1 3.14159... 3 0.14159... 0.14159... 2 12.56637... 13 -0.43362... 0.43362... 3 28.27433... 28 0.27433... 0.27433... 4 50.26548... 50 0.26548... 0.26548... 5 78.53981... 79 -0.46018... 0.46018... 6 113.09733... 113 0.09733... 0.09733... 7 153.93804... 154 -0.06195... 0.06195... ... a(1) = 1. 2, 3, 4 and 5 are not in the sequence, because their absolute errors e are greater than that of a(1). 6 is in the sequence, because its absolute error e is less than that of a(1), therefore a(2) = 6. 7 is in the sequence, because its absolute error e is less than that of a(2), therefore a(3) = 7. ...
Crossrefs
Cf. A067561.
Programs
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PARI
{m=1;for(n=1,10^10,c=Pi*n^2;e=abs(c-round(c));if(e
Comments