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

 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, PARI program for A301626 Wikipedia, Gaussian integer Wikipedia, Voronoi diagram 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.

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