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 A020655 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 5. 28
 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 126, 127, 128, 129, 131, 132, 133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE Noap:= proc(N, m) # N terms of earliest increasing seq with no m-term arithmetic progression local A, forbid, n, c, ds, j; A:= Vector(N): A[1..m-1]:= <(\$1..m-1)>: forbid:= {m}: for n from m to N do   c:= min({\$A[n-1]+1..max(max(forbid)+1, A[n-1]+1)} minus forbid);   A[n]:= c;   ds:= convert(map(t -> c-t, A[m-2..n-1]), set);   for j from m-2 to 2 by -1 do     ds:= ds intersect convert(map(t -> (c-t)/j, A[m-j-1..n-j]), set);     if ds = {} then break fi;   od;   forbid:= select(`>`, forbid, c) union map(`+`, ds, c); od: convert(A, list) end proc: Noap(100, 5); # Robert Israel, Jan 04 2016 MATHEMATICA t = {1, 2, 3, 4}; Do[s = Table[Append[i, n], {i, Subsets[t, {4}]}]; If[! MemberQ[Table[Differences[i, 2], {i, s}], {0, 0, 0}], AppendTo[t, n]], {n, 5, 100}]; t (* T. D. Noe, Apr 17 2014 *) CROSSREFS Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first): 3-term AP: A005836 (>=0), A003278 (>0); 4-term AP: A005839 (>=0), A005837 (>0); 5-term AP: A020654 (>=0), A020655 (>0); 6-term AP: A020656 (>=0), A005838 (>0); 7-term AP: A020657 (>=0), A020658 (>0); 8-term AP: A020659 (>=0), A020660 (>0); 9-term AP: A020661 (>=0), A020662 (>0); 10-term AP: A020663 (>=0), A020664 (>0). Sequence in context: A101888 A190241 A225859 * A188042 A236842 A236860 Adjacent sequences:  A020652 A020653 A020654 * A020656 A020657 A020658 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 20 11:17 EDT 2019. Contains 328257 sequences. (Running on oeis4.)