OFFSET
1,2
COMMENTS
a(n) = A005839(n) + 1. - Alois P. Heinz, Jan 31 2014
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..1001 from Alois P. Heinz)
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.
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, 4); # Robert Israel, Jan 04 2016
MATHEMATICA
t = {1, 2, 3}; Do[s = Table[Append[i, n], {i, Subsets[t, {3}]}]; If[! MemberQ[Table[Differences[i, 2], {i, s}], {0, 0}], AppendTo[t, n]], {n, 4, 200}]; t (* T. D. Noe, Apr 17 2014 *)
CROSSREFS
Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Jan 03 2016. Further edited (with new offset) by N. J. A. Sloane, Jan 04 2016
STATUS
approved