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 A020658 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 7. 29
 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 99 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is different from A047304: note the gap between 41 and 50. - M. F. Hasler, Oct 07 2014 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n)=A020657(n)+1. - M. F. Hasler, Oct 07 2014 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, 7); # Robert Israel, Jan 04 2016 CROSSREFS Cf. A047304. 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: A187396 A020659 A047304 * A195178 A043092 A023801 Adjacent sequences:  A020655 A020656 A020657 * A020659 A020660 A020661 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)