login
A301639
a(n) = square of the distance from n to nearest cube of a Gaussian integer.
2
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.
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
Sequence in context: A153109 A198736 A117180 * A123531 A201522 A368040
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 25 2018
STATUS
approved