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1
Number of new penny-penny contacts when putting pennies on a table following a spiral pattern.
+10
6
0, 1, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3
The maximum number of occurrences of the same distance among n points in the plane.
+10
4
0, 1, 3, 5, 7, 9, 12, 14, 18, 20, 23, 27, 30, 33
Maximum over all sets of n points in the plane of the number of second-smallest distances between the points.
+10
3
0, 0, 2, 4, 6, 9, 11, 14, 18, 20
Start a spiral of numbers on a hexagonal tiling, with the initial hexagon as a(1) = 1. a(n) is the smallest positive integer not equal to or previously adjacent to its neighbors.
+10
2
1, 2, 3, 4, 5, 6, 7, 4, 6, 8, 5, 9, 8, 10, 2, 11, 3, 10, 11, 12, 13, 9, 12, 7, 13, 14, 1, 11, 13, 15, 9, 16, 14, 7, 16, 17, 15, 1, 16, 18, 7, 17, 19, 20, 1, 17, 18, 19, 9, 21, 3, 20, 10, 22, 4, 15, 21, 23, 5, 22, 23, 10, 21, 6, 22, 24, 25, 2, 14, 22, 25, 26, 3
The maximum number of penny-to-penny connections when n pennies are placed on the vertices of a hexagonal tiling.
+10
1
0, 0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 81, 83, 84, 86, 87, 89, 90
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