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%I #18 Oct 29 2021 05:59:37
%S 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,
%T 66,70,14,19,21,49,54,68,71,72,28,30,35,50,60,69,79,81,194,29,33,36,
%U 52,63,74,80,153,195,208,31,34,44,53,64,75,151,162,197,209
%N 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.
%C a(n, 1) is the least positive integer not in a previous row.
%C This sequence is a permutation of the natural numbers.
%C The first row is A003278.
%C The second row is the lexicographically earliest sequence of terms not in the first row that contains no arithmetic progressions.
%C The third row is the lexicographically earliest sequence of terms not in the first two rows that contains no arithmetic progressions.
%H Peter Kagey, <a href="/A293030/b293030.txt">First 90 rows, flattened</a>
%e a(2, 4) = 12 because row 2 begins (3, 6, 7)
%e a(2, 4) != 8 because (6, 7, 8) is an arithmetic progression,
%e a(2, 4) != 9 because (3, 6, 9) is an arithmetic progression,
%e a(2, 4) != 10 because a(1, 5) = 10 is in a previous row.
%e a(2, 4) != 11 because a(1, 6) = 11 is in a previous row.
%e a(2, 4) = 12 does not create any arithmetic progressions in row 2, and 12 is not in row 1.
%e Array begins:
%e 1 2 4 5 10 11 13 14 28 29 ...
%e 3 6 7 12 15 16 19 30 33 34 ...
%e 8 9 17 18 20 21 35 36 44 45 ...
%e 22 23 25 26 49 50 52 53 58 59 ...
%e 24 27 51 54 60 63 64 67 73 76 ...
%e 65 66 68 69 74 75 77 78 146 147 ...
%e 70 71 79 80 151 152 160 161 178 179 ...
%e 72 81 153 162 180 189 192 193 196 201 ...
%e 194 195 197 198 203 204 206 207 221 222 ...
%e 208 209 211 212 235 236 238 239 451 452 ...
%e ...
%Y Cf. A003278.
%K nonn,tabl,look
%O 1,2
%A _Peter Kagey_, Sep 28 2017
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