login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A301626 Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0: T(n, k) = square of the distance from n + k*i to nearest cube of a Gaussian integer (where i denotes the root of -1 with positive imaginary part). 3
0, 0, 0, 1, 1, 1, 4, 1, 1, 4, 8, 2, 0, 2, 8, 9, 5, 1, 1, 5, 9, 4, 10, 4, 2, 4, 10, 4, 1, 5, 9, 5, 5, 9, 5, 1, 0, 2, 8, 10, 8, 10, 8, 2, 0, 1, 1, 5, 13, 13, 13, 13, 5, 1, 1, 4, 2, 4, 10, 20, 18, 20, 10, 4, 2, 4, 4, 2, 4, 9, 17, 25, 25, 17, 9, 4, 2, 4, 5, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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

This sequence is a complex variant of A074989.

See A301636 for the square array dealing with squares of Gaussian integers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..20300

Rémy Sigrist, Colored scatterplot for abs(x) <= 500 and abs(y) <= 500 (where the hue is function of sqrt(T(abs(x), abs(y))))

Rémy Sigrist, Voronoi diagram of the cubes of Gaussian integers for abs(x) <= 500 and abs(y) <= 500

Rémy Sigrist, Scatterplot of (x, y) such that T(abs(x), abs(y)) is a square and abs(x) <= 500 and abs(y) <= 500

Rémy Sigrist, PARI program for A301626

Wikipedia, Gaussian integer

Wikipedia, Voronoi diagram

Index entries for sequences related to distance to nearest element of some set

FORMULA

T(n, k) = T(k, n).

T(n, 0) <= A074989(n)^2.

T(n, 0) = 0 iff n is a cube (A000578).

T(n, k) = 0 iff n + k*i = z^3 for some Gaussian integer z.

EXAMPLE

Square array begins:

  n\k|    0    1    2    3    4    5    6    7    8    9   10

  ---+-------------------------------------------------------

    0|    0    0    1    4    8    9    4    1    0    1    4  -->  A301639

    1|    0    1    1    2    5   10    5    2    1    2    2

    2|    1    1    0    1    4    9    8    5    4    4    1

    3|    4    2    1    2    5   10   13   10    9    5    2

    4|    8    5    4    5    8   13   20   17   13    8    5

    5|    9   10    9   10   13   18   25   25   18   13   10

    6|    4    5    8   13   20   25   32   32   25   20   17

    7|    1    2    5   10   17   25   32   41   34   29   26

    8|    0    1    4    9   13   18   25   34   45   40   37

    9|    1    2    4    5    8   13   20   29   40   53   50

   10|    4    2    1    2    5   10   17   26   37   50   65

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000578, A074989, A301636, A301639 (first row/column).

Sequence in context: A026998 A326812 A324893 * A080061 A246595 A209571

Adjacent sequences:  A301623 A301624 A301625 * A301627 A301628 A301629

KEYWORD

nonn,tabl,look

AUTHOR

Rémy Sigrist, Mar 24 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 20:11 EST 2020. Contains 331288 sequences. (Running on oeis4.)