

A087060


Difference between 2n^2 and the nearest square number.


7



1, 1, 2, 4, 1, 8, 2, 7, 7, 4, 14, 1, 14, 8, 9, 17, 2, 23, 7, 16, 18, 7, 31, 4, 25, 17, 14, 32, 1, 36, 14, 23, 31, 8, 49, 9, 34, 28, 17, 49, 2, 47, 23, 28, 46, 7, 62, 16, 41, 41, 18, 68, 7, 56, 34, 31, 63, 4, 73, 25, 46, 56, 17, 89, 14, 63, 47, 32, 82, 1, 82, 36, 49, 73, 14, 103, 23, 68
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OFFSET

1,3


COMMENTS

max(a(n)/n) approaches sqrt(2), and the indices of the maxima are apparently in A227792.  Ralf Stephan, Sep 23 2013


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = min [A087056(n), A087059(n)] = min [2*n^2  (floor[n*sqrt(2)])^2, (1 + floor[n*sqrt(2)])^2  2*n^2]


EXAMPLE

a(10) = 4 because the difference between 2*10^2 = 200 and the nearest square number (196) is 4.


MATHEMATICA

dnsn[n_]:=Module[{c=2n^2, a, b}, a=Floor[Sqrt[c]]^2; b=Ceiling[Sqrt[c]]^2; Min[ca, bc]]; Array[dnsn, 80] (* Harvey P. Dale, Jul 01 2017 *)


CROSSREFS

Cf. A001951, A087055, A087056, A087057, A087058, A087059.
Sequence in context: A221073 A181266 A302192 * A248112 A173122 A232723
Adjacent sequences: A087057 A087058 A087059 * A087061 A087062 A087063


KEYWORD

easy,nonn,look


AUTHOR

Jens Voß, Aug 07 2003


STATUS

approved



