A240557 Earliest positive increasing sequence with no 5-term subsequence of constant third differences.

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

Offset: 1

Author

T. D. Noe, Apr 09 2014

Keywords

• nonn

Comments

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

Crossrefs

Cf. A240556 (starting with 0).

No 3-term AP: A005836 (>=0), A003278 (>0);

no 4-term AP: A240075 (>=0), A240555 (>0);

no 5-term AP: A020654 (>=0), A020655 (>0);

no 6-term AP: A020656 (>=0), A005838 (>0);

no 7-term AP: A020657 (>=0), A020658 (>0);

no 8-term AP: A020659 (>=0), A020660 (>0);

no 9-term AP: A020661 (>=0), A020662 (>0);

no 10-term AP: A020663 (>=0), A020664 (>0).

Cf. A240075 and A240555 for sequences avoiding 4-term subsequences with constant second differences.

Programs

Mathematica

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

PARI

A240557(n,show=0,L=5,o=3,v=[1],D=v->v[2..-1]-v[1..-2])={ my(d,m); while( #v1,);#Set(d)>1||next(2),2);break));v[#v]} \\ M. F. Hasler, Jan 12 2016

Extensions

Definition corrected by M. F. Hasler, Jan 12 2016