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A005839 Lexicographically earliest increasing nonnegative sequence that contains no 4-term arithmetic progression.

%I A005839 M0956 #41 Jan 09 2016 12:01:50
%S A005839 0,1,2,4,5,7,8,9,14,15,16,18,25,26,28,29,30,33,36,48,49,50,52,53,55,
%T A005839 56,57,62,64,65,66,79,86,87,88,90,93,98,101,104,105,108,109,110,121,
%U A005839 125,135,144,148,150,151,159,162,166,168,169,170,173,175,176,182
%N A005839 Lexicographically earliest increasing nonnegative sequence that contains no 4-term arithmetic progression.
%C A005839 a(n) = A005837(n) - 1. - _Alois P. Heinz_, Jan 31 2014
%D A005839 R. K. Guy, Unsolved Problems in Number Theory, E10.
%D A005839 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005839 David W. Wilson, <a href="/A005839/b005839.txt">Table of n, a(n) for n = 1..10000</a> a(1..1001) from _Alois P. Heinz_
%t A005839 t = {0, 1, 2}; Do[s = Table[Append[i, n], {i, Subsets[t, {3}]}];
%t A005839 If[! MemberQ[Table[Differences[i, 2], {i, s}], {0, 0}], AppendTo[t, n]], {n, 3, 200}]; t (* _T. D. Noe_, Apr 17 2014 *)
%Y A005839 Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
%Y A005839 3-term AP: A005836 (>=0), A003278 (>0);
%Y A005839 4-term AP: A005839 (>=0), A005837 (>0);
%Y A005839 5-term AP: A020654 (>=0), A020655 (>0);
%Y A005839 6-term AP: A020656 (>=0), A005838 (>0);
%Y A005839 7-term AP: A020657 (>=0), A020658 (>0);
%Y A005839 8-term AP: A020659 (>=0), A020660 (>0);
%Y A005839 9-term AP: A020661 (>=0), A020662 (>0);
%Y A005839 10-term AP: A020663 (>=0), A020664 (>0).
%K A005839 nonn
%O A005839 1,3
%A A005839 _N. J. A. Sloane_
%E A005839 More terms from _Jeffrey Shallit_, Aug 15 1995.
%E A005839 Edited (with new offset, etc.) by _N. J. A. Sloane_, Jan 04 2016