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A020660 Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 8. 28
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 84, 85, 87, 88, 89, 91, 92, 93, 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, 8); # 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: A023750 A091249 A154799 * A047306 A283970 A121166

Adjacent sequences:  A020657 A020658 A020659 * A020661 A020662 A020663

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 19 05:12 EST 2018. Contains 299330 sequences. (Running on oeis4.)