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
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
KEYWORD
nonn
AUTHOR
Gordon Hamilton, Oct 28 2021
EXTENSIONS
More terms from David A. Corneth, Nov 03 2021 (computed from A265316).
STATUS
approved