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A240557
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Earliest positive increasing sequence with no 5-term subsequence of constant third differences.
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12
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1, 2, 3, 4, 6, 8, 12, 16, 17, 28, 48, 49, 65, 96, 176, 197, 212, 213, 215, 248, 250, 253, 399, 840, 1003, 1015, 1017, 1036, 1037, 1038, 1052, 1055, 1073, 1122, 1144, 1147, 1173, 1259, 4272, 4283, 4285, 4337, 4572, 4579, 4583, 4599, 4614, 4623, 4629, 4647
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OFFSET
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1,2
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COMMENTS
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For the nonnegative sequence, see A240556, which is this sequence minus 1. Is there a simple way of determining this sequence, as in the case of the no 3-term arithmetic progression?
See crossreferences for sequences avoiding arithmetic progressions. - M. F. Hasler, Jan 12 2016
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LINKS
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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[Flatten[Table[Differences[i, 4], {i, s}]], 0], AppendTo[t, n]], {n, 5, 5000}]; t
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PROG
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(PARI) A240557(n, show=0, L=5, o=3, v=[1], D=v->v[2..-1]-v[1..-2])={ my(d, m); while( #v<n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while( v[#v]++, forvec( i=vector(L, j, [if(j<L, j, #v), #v]), d=D(vecextract(v, i)); m=o; while(m--&&#Set(d=D(d))>1, ); #Set(d)>1||next(2), 2); break)); v[#v]} \\ M. F. Hasler, Jan 12 2016
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CROSSREFS
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Cf. A240075 and A240555 for sequences avoiding 4-term subsequences with constant second differences.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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