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 A005838 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 6. (Formerly M0516) 28
 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 33, 34, 35, 36, 37, 39, 43, 44, 45, 46, 47, 49, 50, 51, 52, 59, 60, 62, 63, 64, 65, 66, 68, 69, 71, 73, 77, 85, 87, 88, 89, 90, 91, 93, 96, 97, 98, 99, 100, 103, 104, 107, 111, 114, 115, 117, 118, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 J. L. Gerver and L. T. Ramsey, Sets of integers with no long arithmetic progressions generated by the greedy algorithm, Math. Comp. 33 (1979), 1353-1359. FORMULA a(n) = A020656(n) + 1. MAPLE N:= 100: # to get a(1)..a(N) A:= Vector(N): A[1..5]:= <(\$1..5)>: forbid:= {6}: for n from 6 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[4..n-1], set);   if ds = {} then next fi;   ds:= ds intersect convert(map(t -> (c-t)/4, A[1..n-4]), set);   if ds = {} then next fi;   ds:= ds intersect convert(map(t -> (c-t)/3, A[2..n-3]), set);   if ds = {} then next fi;   ds:= ds intersect convert(map(t -> (c-t)/2, A[3..n-2]), set);   forbid:= select(`>`, forbid, c) union map(`+`, ds, c); od: convert(A, list); # Robert Israel, Jan 04 2016 PROG (PARI) A005838(n, show=1, i=1, o=6, u=0)={for(n=1, n, show&&print1(i, ", "); u+=1<=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: A032797 A001967 A226066 * A184486 A047203 A080919 Adjacent sequences:  A005835 A005836 A005837 * A005839 A005840 A005841 KEYWORD nonn AUTHOR EXTENSIONS Name and links/references edited by M. F. Hasler, Jan 03 2016 Further edited by N. J. A. Sloane, Jan 04 2016 STATUS approved

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