%I A003002 M0275
%S A003002 1,2,2,3,4,4,4,4,5,5,6,6,7,8,8,8,8,8,8,9,9,9,9,10,10,11,11,11,11,12,12,
%T A003002 13,13,13,13,14,14,14,14,15,16,16,16,16,16,16,16,16,16,16,17,17,17,18,
%U A003002 18,18,18,19,19,19,19,19,20,20,20,20,20,20,20,20,21,21,21,22,22,22,22
%N A003002 Size of the largest subset of the numbers [1...n] which doesn't contain 
               a 3-term arithmetic progression.
%C A003002 These subsets have been called 3-free sequences.
%C A003002 Actually, more terms of this sequence can be found directly from A065825, 
               because A003002(n) (this sequence) = the integer k such that A065825(k) 
               <= n < A065825(k+1). [From R. Shreevatsa (shreevatsa.public(AT)gmail.com), 
               Oct 18 2009]
%D A003002 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003002 S. S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 
               (1972), 767-771.
%Y A003002 Cf. A003003, A003004, A003005, A065825.
%Y A003002 Sequence in context: A029130 A081611 A081228 this_sequence A087180 A029121 
               A161205
%Y A003002 Adjacent sequences: A002999 A003000 A003001 this_sequence A003003 A003004 
               A003005
%K A003002 nonn
%O A003002 1,2
%A A003002 N. J. A. Sloane (njas(AT)research.att.com).
%E A003002 Extended from 53 terms to 80 terms, using a simple brute-force program 
               with some pruning. R. Shreevatsa (shreevatsa.public(AT)gmail.com), 
               Oct 18 2009