A301639 a(n) = square of the distance from n to nearest cube of a Gaussian integer.

0, 0, 1, 4, 8, 9, 4, 1, 0, 1, 4, 4, 5, 8, 13, 20, 29, 40, 53, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 130, 117, 106, 97, 90, 85, 82, 81, 82, 85, 90, 97, 106, 117, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25

Offset: 0

Author

Rémy Sigrist, Mar 25 2018

Keywords

• nonn

Comments

The distance between two Gaussian integers is not necessarily integer, hence the use of the square of the distance.

This sequence is a variant of A074989: here we minimize norm(n - z^3) where z runs through every Gaussian integers, there we minimize abs(n - m^3) where m runs through every integers.

Examples

			For n = 4: the nearest Gaussian cubes to 4 are 2 + 2*i and 2 - 2*i, hence a(4) = (4-2)^2 + 2^2 = 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Scatterplot of this sequence versus A074989^2 for n = 0..1000
• Wikipedia, Gaussian integer
• Index entries for sequences related to distance to nearest element of some set

Crossrefs

Cf. A074989, A301626.

Formula

a(n) = A301626(n, 0).

a(n) <= A074989(n)^2.