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A225073 Location (x,y) of the first n x n square of composite Gaussian integers in the first quadrant. 3
0, 0, 3, 3, 3, 12, 9, 35, -2, 48, 65, 72, 65, 72, 73, 183, 357, 500, 357, 500, 480, 1250, 2201, 2201, -6, 4347, 4426, 4226, 9911, 13005, 20871, 22511 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The location of the bottom-left corner of the square is given. We choose the x-coordinate to be as small as possible. The x-coordinate can be negative if the n x n square is centered on the y-axis, as is the case for n = 5 and n = 13. The square is on the line y = x when n = 1, 2, 12, and 14. The Mathematica program prints the minimum (x,y) point and its squared distance from the origin.

LINKS

Table of n, a(n) for n=1..32.

T. D. Noe, Plot of composite squares

MATHEMATICA

nn = 1000; offset = 15; z = Table[If[PrimeQ[i + j*I, GaussianIntegers -> True], 1, 0], {i, -offset, nn}, {j, -offset, nn}]; off1 = offset + 1; done = False; sz = 0; While[! done, sz++; mn = Infinity; best = {}; Do[sm = 0; Do[sm = sm + z[[i + ii - 1, j + jj - 1]]; If[sm > 0, Break[]], {ii, sz}, {jj, sz}]; If[sm == 0, d = (i - off1)^2 + (j - off1)^2; If[d <= mn, mn = d; best = {i - off1, j - off1}]], {i, off1 - sz, nn - 1}, {j, i, nn - 1}]; If[mn < Infinity, Print[{Sort[best], mn}], done = True]]

CROSSREFS

Cf. A225074 (x coordinates), A225075 (y coordinates).

Sequence in context: A101480 A156715 A133797 * A152575 A170851 A052900

Adjacent sequences:  A225070 A225071 A225072 * A225074 A225075 A225076

KEYWORD

sign,more,hard

AUTHOR

T. D. Noe, May 04 2013

STATUS

approved

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Last modified July 27 13:22 EDT 2021. Contains 346306 sequences. (Running on oeis4.)