A341278 The smallest spiral number not covered by any square in the minimal-sum square spiral tiling by n X n squares in A341363.

67, 173, 25, 30, 42, 56, 72, 90, 110, 132, 156, 182, 209, 239, 271, 305, 341, 379, 419, 461, 505, 551, 599, 649, 701, 755, 810, 860, 928, 990, 1054, 1120, 1188, 1258, 1330, 1404, 1480, 1558, 1638, 1720, 1804, 1890, 1978, 2067, 2159, 2253, 2349, 2447, 2547, 2649, 2753, 2859, 2967, 3077, 3189

Offset: 2

Author

Scott R. Shannon, Feb 08 2021

Keywords

• nonn

Comments

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.

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

Links

• Scott R. Shannon, Image of the tiling for n=2. 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.
• Scott R. Shannon, Image of the tiling for n=3. The smallest uncovered square is 173.
• Scott R. Shannon, Image of the tiling for n=4. The smallest uncovered square is 25.
• Scott R. Shannon, Image of the tiling for n=5. The smallest uncovered square is 30.
• Scott R. Shannon, Image of the tiling for n=6. The smallest uncovered square is 42.

Crossrefs

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