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

1,2

Comments

Inspired by A067561.

Links

Table of n, a(n) for n=1..27.

Example

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.
...

Prog

(PARI){m=1; for(n=1, 10^10, c=Pi*n^2; e=abs(c-round(c)); if(e<m, m=e; print1(n, ", ")))}

Crossrefs

Cf. A067561.

Sequence in context: A112813 A347808 A048018 * A047197 A048079 A011346

Adjacent sequences: A254711 A254712 A254713 * A254715 A254716 A254717

Keyword

nonn

Author

Kival Ngaokrajang, Feb 06 2015

Status

approved