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 A301636 Square array T(n, k) read by antidiagonals upwards, n >= 0 and k >= 0: T(n, k) = square of the distance from n + k*i to nearest square of a Gaussian integer (where i denotes the root of -1 with positive imaginary part). 2
 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 2, 4, 2, 4, 1, 1, 4, 2, 4, 9, 4, 2, 4, 1, 1, 5, 4, 4, 5, 5, 2, 0, 2, 5, 1, 1, 5, 8, 5, 1, 1, 5, 2, 0, 0, 2, 8, 10, 4, 2, 4, 5, 1, 1, 1, 1, 5, 10, 8, 5, 5, 9, 4, 2, 4, 4, 2, 4, 9, 5, 5, 8, 10, 9, 5, 5, 9, 9, 5, 5, 9, 4, 2, 4, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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 A053188. See A301626 for the square array dealing with cubes of Gaussian integers. LINKS 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 A301636 Wikipedia, Gaussian integer Wikipedia, Voronoi diagram FORMULA T(n, 0) <= A053188(n)^2. T(n, 0) = 0 iff n is a square (A000290). T(0, k) = 0 iff k is twice a square (A001105). T(n, k) = 0 iff n + k*i = z^2 for some Gaussian integer z. EXAMPLE Square array begins:   n\k|    0    1    2    3    4    5    6    7    8    9   10   ---+-------------------------------------------------------     0|    0    1    0    1    4    9    4    1    0    1    4     1|    0    1    1    2    4    5    5    2    1    2    5     2|    1    2    4    2    1    2    5    5    4    5    8     3|    1    2    4    1    0    1    4    9    9   10    8     4|    0    1    4    2    1    2    5   10   16   10    5     5|    1    2    5    5    4    5    8   10   13    9    4     6|    4    5    8   10    8    5    4    5    8   10    5     7|    4    5    8   10    5    2    1    2    5   10    8     8|    1    2    5    9    4    1    0    1    4    9   13     9|    0    1    4    9    5    2    1    2    5   10   17    10|    1    2    5   10    8    5    4    5    8   13   20 PROG (PARI) See Links section. CROSSREFS Cf. A000290, A001105, A053188, A301626. Sequence in context: A267486 A285229 A227425 * A238857 A253587 A110962 Adjacent sequences:  A301633 A301634 A301635 * A301637 A301638 A301639 KEYWORD nonn,tabl AUTHOR Rémy Sigrist, Mar 25 2018 STATUS approved

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Last modified January 28 13:24 EST 2020. Contains 331321 sequences. (Running on oeis4.)