%I A003004 M0451
%S A003004 1,2,3,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,16,16,16,16,17,18,18,
%T A003004 19,20,21,21,22,22,23,24,24,25,26,27,28,28,29,30,31,32,32,32,32,32,33,
               33
%N A003004 Size of the largest subset of the numbers [1...n] which does not contain 
               a 5-term arithmetic progression.
%C A003004 These subsets have been called 5-free sequences.
%C A003004 The g.f. (z+1)*(1+z**2)/(z**4+z**3+z**2+z+1)/(z-1)**2 conjectured by 
               S. Plouffe in his 1992 dissertation is wrong.
%D A003004 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003004 S. S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 
               (1972), 767-771.
%H A003004 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003004 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%Y A003004 Cf. A003002, A003003, A003005, A065825.
%Y A003004 Sequence in context: A006162 A036701 A053756 this_sequence A120507 A090223 
               A109401
%Y A003004 Adjacent sequences: A003001 A003002 A003003 this_sequence A003005 A003006 
               A003007
%K A003004 nonn
%O A003004 1,2
%A A003004 N. J. A. Sloane (njas(AT)research.att.com).