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 A020662 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 9. 28
 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 53, 55, 56, 57, 58, 59, 60, 64, 65, 66, 67, 68, 69, 70, 71, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 91, 92, 94, 95, 96, 97 (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, 9); # Robert Israel, Jan 04 2016 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: A043094 A023803 A122132 * A302569 A235034 A107037 Adjacent sequences:  A020659 A020660 A020661 * A020663 A020664 A020665 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 18 09:00 EST 2019. Contains 319269 sequences. (Running on oeis4.)