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

1,2

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).

Links

Table of n, a(n) for n=1..47.

MathPickle, Hare vs. Hare, 2017.

Formula

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

Example

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

Crossrefs

Cf. A003278, A005836.

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

Sequence in context: A353424 A156291 A111136 * A063937 A363593 A178525

Adjacent sequences: A348633 A348634 A348635 * A348637 A348638 A348639

Keyword

nonn

Author

Gordon Hamilton, Oct 28 2021

Extensions

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

Status

approved