A348636 Greedy Cantor's Dust Partition.

1, 3, 8, 22, 24, 65, 70, 72, 194, 208, 210, 215, 580, 582, 623, 628, 630, 644, 1738, 1740, 1745, 1867, 1869, 1883, 1888, 1890, 1931, 5212, 5214, 5219, 5233, 5235, 5600, 5605, 5607, 5648, 5662, 5664, 5669, 5791, 5793, 15635, 15640, 15642, 15656, 15697, 15699

Offset: 1

Author

Gordon Hamilton, Oct 28 2021

Keywords

• nonn

Comments

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).

Examples

			S(1) = Cantor's dust 1,2,4,5,10,11,13,14,28,29,31,32,... (A003278)
S(2) = 3,6,7,12,15,16,19,30,33,34,...
S(3) = 8,9,17,18,20,21,35,36,44,...
S(4) = 22,23,25,26,49,50,52,53,...
S(5) = 24,27,51,54,60,63,64,67,...
S(6) = 65,66,68,69,...
S(7) = 70,71,...
S(8) = 72,...
a(1) = min [S(1)] = 1
a(2) = min [S(2)] = 3
a(3) = min [S(3)] = 8
a(4) = min [S(4)] = 22
a(5) = min [S(5)] = 24
a(6) = min [S(6)] = 65
a(7) = min [S(7)] = 70
a(8) = min [S(8)] = 72
		

Links

• MathPickle, Hare vs. Hare, 2017.

Crossrefs

Cf. A003278, A005836.

One more than A265316, which is the first row of A262057.

Formula

a(n) = A265316(n) + 1.

Extensions

More terms from David A. Corneth, Nov 03 2021 (computed from A265316).