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A282510
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Irregular triangle T(n,k) read by rows: Each term is the least positive integer such that no row, column, diagonal, or antidiagonal contains a repeated term; and each row terminates at k when it contains all numbers <= k.
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1
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1, 2, 3, 1, 4, 5, 2, 3, 1, 3, 1, 4, 5, 2, 5, 2, 3, 1, 4, 6, 4, 5, 2, 3, 7, 8, 9, 1, 7, 8, 6, 4, 5, 9, 10, 11, 2, 3, 1, 9, 10, 7, 8, 6, 11, 12, 13, 4, 5, 2, 3, 1, 8, 6, 9, 10, 7, 13, 14, 15, 11, 12, 4, 5, 2, 3, 1, 10, 11, 12, 6, 9, 1, 7, 8, 13, 14, 15, 16, 4, 5, 2, 3
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OFFSET
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1,2
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COMMENTS
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Similar in construction to A274651; the difference between them is that here, each row terminates at k when it contains all numbers <= k (hence this triangle is irregular, while A274651 is not).
Conjecture: All columns and diagonals are permutations of the natural numbers; a proof will be more involved than for A274651.
Row lengths are not (weakly) monotonically increasing: row 25 has 42 terms, row 26 has 41 terms. Row indices where row lengths decrease are: 26, 64, 144, 199, 326, 400, ... . - Alois P. Heinz, Mar 17 2017
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LINKS
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EXAMPLE
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Triangle begins:
: 1
: 2 3 1
: 4 5 2 3 1
: 3 1 4 5 2
: 5 2 3 1 4
: 6 4 5 2 3 7 8 9 1
: 7 8 6 4 5 9 10 11 2 3 1
: 9 10 7 8 6 11 12 13 4 5 2 3 1
: 8 6 9 10 7 13 14 15 11 12 4 5 2 3 1
: 10 11 12 6 9 1 7 8 13 14 15 16 4 5 2 3
: 12 7 13 14 8 2 3 1 6 10 9 17 11 15 4 5 16
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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