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A020655
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Lexicographically earliest increasing sequence of positive numbers that contains no arithmetic progression of length 5.
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28
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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)
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OFFSET
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1,2
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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