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

Author

Ralf Stephan, Sep 23 2013

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A001951, A087060.

Programs

PARI

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

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].