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

0,4

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.

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

Formula

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

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

Example

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.

Crossrefs

Cf. A074989, A301626.

Sequence in context: A153109 A198736 A117180 * A123531 A201522 A368040

Adjacent sequences: A301636 A301637 A301638 * A301640 A301641 A301642

Keyword

nonn

Author

Rémy Sigrist, Mar 25 2018

Status

approved