A087060 Difference between 2n^2 and the nearest square number.

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

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[c-a, b-c]]; 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