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The smallest spiral number not covered by any square in the minimal-sum square spiral tiling by n X n squares in A341363.
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%I #15 Feb 14 2021 13:17:47

%S 67,173,25,30,42,56,72,90,110,132,156,182,209,239,271,305,341,379,419,

%T 461,505,551,599,649,701,755,810,860,928,990,1054,1120,1188,1258,1330,

%U 1404,1480,1558,1638,1720,1804,1890,1978,2067,2159,2253,2349,2447,2547,2649,2753,2859,2967,3077,3189

%N The smallest spiral number not covered by any square in the minimal-sum square spiral tiling by n X n squares in A341363.

%C The tilings with n=2 and n=3 are the only ones where the smallest uncovered square is not adjacent to the first centrally placed tile. The sequence starts at n=2 as a 1 X 1 square tiling leaves no squares uncovered.

%C See A341363 for other images with higher numbers of placed tiles.

%H Scott R. Shannon, <a href="/A341278/a341278.png">Image of the tiling for n=2</a>. The smallest uncovered square is 67. In this and other images the colors are graduated around the spectrum to show the squares relative placement order.

%H Scott R. Shannon, <a href="/A341278/a341278_1.png">Image of the tiling for n=3</a>. The smallest uncovered square is 173.

%H Scott R. Shannon, <a href="/A341278/a341278_2.png">Image of the tiling for n=4</a>. The smallest uncovered square is 25.

%H Scott R. Shannon, <a href="/A341278/a341278_3.png">Image of the tiling for n=5</a>. The smallest uncovered square is 30.

%H Scott R. Shannon, <a href="/A341278/a341278_4.png">Image of the tiling for n=6</a>. The smallest uncovered square is 42.

%Y Cf. A341363, A341160, A341327, A340974, A174344, A274923, A296030, A275161.

%K nonn

%O 2,1

%A _Scott R. Shannon_, Feb 08 2021