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A293030
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Square array read by antidiagonals downwards: a(n, k) is smallest number m > a(n, k-1) that is not in a previous row, and that avoids any 3-term arithmetic progression in a(n, 1), a(n, 2), ..., a(n, k-1), m.
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1
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1, 2, 3, 4, 6, 8, 5, 7, 9, 22, 10, 12, 17, 23, 24, 11, 15, 18, 25, 27, 65, 13, 16, 20, 26, 51, 66, 70, 14, 19, 21, 49, 54, 68, 71, 72, 28, 30, 35, 50, 60, 69, 79, 81, 194, 29, 33, 36, 52, 63, 74, 80, 153, 195, 208, 31, 34, 44, 53, 64, 75, 151, 162, 197, 209
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OFFSET
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1,2
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COMMENTS
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a(n, 1) is the least positive integer not in a previous row.
This sequence is a permutation of the natural numbers.
The second row is the lexicographically earliest sequence of terms not in the first row that contains no arithmetic progressions.
The third row is the lexicographically earliest sequence of terms not in the first two rows that contains no arithmetic progressions.
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LINKS
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EXAMPLE
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a(2, 4) = 12 because row 2 begins (3, 6, 7)
a(2, 4) != 8 because (6, 7, 8) is an arithmetic progression,
a(2, 4) != 9 because (3, 6, 9) is an arithmetic progression,
a(2, 4) != 10 because a(1, 5) = 10 is in a previous row.
a(2, 4) != 11 because a(1, 6) = 11 is in a previous row.
a(2, 4) = 12 does not create any arithmetic progressions in row 2, and 12 is not in row 1.
Array begins:
1 2 4 5 10 11 13 14 28 29 ...
3 6 7 12 15 16 19 30 33 34 ...
8 9 17 18 20 21 35 36 44 45 ...
22 23 25 26 49 50 52 53 58 59 ...
24 27 51 54 60 63 64 67 73 76 ...
65 66 68 69 74 75 77 78 146 147 ...
70 71 79 80 151 152 160 161 178 179 ...
72 81 153 162 180 189 192 193 196 201 ...
194 195 197 198 203 204 206 207 221 222 ...
208 209 211 212 235 236 238 239 451 452 ...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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