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%I #27 Nov 04 2021 22:07:19
%S 1,3,8,22,24,65,70,72,194,208,210,215,580,582,623,628,630,644,1738,
%T 1740,1745,1867,1869,1883,1888,1890,1931,5212,5214,5219,5233,5235,
%U 5600,5605,5607,5648,5662,5664,5669,5791,5793,15635,15640,15642,15656,15697,15699
%N Greedy Cantor's Dust Partition.
%C Starting at 1, consecutively partition the positive integers into sets s(1), s(2), s(3), ... so that no arithmetic sequence of length 3 exists in a set. When choosing s(k), always choose k as small as possible. a(n) = smallest number in s(n).
%H MathPickle, <a href="https://mathpickle.com/project/hare-vs-hare-patterns-algorithm/">Hare vs. Hare</a>, 2017.
%F a(n) = A265316(n) + 1.
%e S(1) = Cantor's dust 1,2,4,5,10,11,13,14,28,29,31,32,... (A003278)
%e S(2) = 3,6,7,12,15,16,19,30,33,34,...
%e S(3) = 8,9,17,18,20,21,35,36,44,...
%e S(4) = 22,23,25,26,49,50,52,53,...
%e S(5) = 24,27,51,54,60,63,64,67,...
%e S(6) = 65,66,68,69,...
%e S(7) = 70,71,...
%e S(8) = 72,...
%e a(1) = min [S(1)] = 1
%e a(2) = min [S(2)] = 3
%e a(3) = min [S(3)] = 8
%e a(4) = min [S(4)] = 22
%e a(5) = min [S(5)] = 24
%e a(6) = min [S(6)] = 65
%e a(7) = min [S(7)] = 70
%e a(8) = min [S(8)] = 72
%Y Cf. A003278, A005836.
%Y One more than A265316, which is the first row of A262057.
%K nonn
%O 1,2
%A _Gordon Hamilton_, Oct 28 2021
%E More terms from _David A. Corneth_, Nov 03 2021 (computed from A265316).
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