A227790 Difference between 3n^2 and the nearest square number.

1, 3, 2, 1, 6, 8, 3, 4, 13, 11, 2, 9, 22, 12, 1, 16, 26, 11, 6, 25, 27, 8, 13, 36, 26, 3, 22, 48, 23, 4, 33, 47, 18, 13, 46, 44, 11, 24, 61, 39, 2, 37, 71, 32, 9, 52, 66, 23, 22, 69, 59, 12, 37, 88, 50, 1, 54, 92, 39, 16, 73, 83, 26, 33, 94, 72, 11, 52, 117, 59, 6, 73, 111, 44, 25, 96, 98, 27, 46, 121

Offset

1,2

Comments

max(a(n)/n) approaches sqrt(3), and the indices of the maxima are apparently in A041017.

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = min (A033428(n)-A022838(n)^2, (1+A022838(n))^2-A033428(n)) = min [3*n^2 - (floor[n*sqrt(3)])^2, (1 + floor[n*sqrt(3)])^2 - 3*n^2].

Example

a(9) = 13 because the difference between 3*9^2 = 243 and the nearest square number (256) is 13.

Prog

(PARI) a(n)=min(3*n^2-(floor(n*sqrt(3)))^2, (1+floor(n*sqrt(3)))^2-3*n^2)

Crossrefs

Cf. A001951, A087060.

Sequence in context: A210858 A114586 A052174 * A181897 A337977 A212207

Adjacent sequences: A227787 A227788 A227789 * A227791 A227792 A227793

Keyword

nonn

Author

Ralf Stephan, Sep 23 2013

Status

approved