A274820 Spiral constructed on the nodes of the infinite triangular net in which each term is the least nonnegative integer such that no diagonal contains a repeated term.
0, 1, 2, 1, 2, 1, 2, 0, 3, 0, 4, 3, 5, 3, 4, 5, 3, 4, 6, 5, 6, 7, 4, 6, 5, 7, 6, 3, 0, 6, 5, 7, 0, 6, 7, 5, 4, 8, 1, 3, 6, 8, 1, 9, 7, 8, 2, 4, 9, 8, 2, 10, 11, 8, 9, 10, 12, 3, 8, 9, 7, 10, 9, 2, 4, 8, 5, 10, 2, 11, 9, 11, 0, 10, 7, 8, 6, 0, 9, 7, 10, 12, 7, 1, 4, 8, 5, 11, 1, 10, 12, 9, 5, 11, 10, 13, 12, 11, 13, 14
Offset: 0
Examples
Illustration of initial terms as a spiral: . . 9 - 4 - 2 - 8 - 7 . / \ . 8 3 - 6 - 7 - 5 9 . / / \ \ . 2 0 5 - 3 - 4 6 1 . / / / \ \ \ . 10 6 3 1 - 2 0 4 8 . / / / / \ \ \ \ . 11 5 4 2 0 - 1 3 7 6 . \ \ \ \ / / / . 8 7 5 1 - 2 - 0 6 3 . \ \ \ / / . 9 0 3 - 4 - 6 - 5 1 . \ \ / . 10 6 - 7 - 5 - 4 - 8 . \ . 12 - 3 - 8 - 9 - 7 .
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..120400
- F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
- Rémy Sigrist, PARI program for A274820
- Rémy Sigrist, Colored illustration of the first 200 windings of the spiral (where the color is a function of a(n))
- N. J. A. Sloane, Illustration of initial terms drawn as a spiral on the hexagonal grid (the starting cell is marked in black).
Crossrefs
Programs
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PARI
See Links section.
Formula
a(n) = A274821(n) - 1.
Comments