cp's OEIS Frontend

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

%I A240557 #18 Feb 27 2018 15:46:11
%S A240557 1,2,3,4,6,8,12,16,17,28,48,49,65,96,176,197,212,213,215,248,250,253,
%T A240557 399,840,1003,1015,1017,1036,1037,1038,1052,1055,1073,1122,1144,1147,
%U A240557 1173,1259,4272,4283,4285,4337,4572,4579,4583,4599,4614,4623,4629,4647
%N A240557 Earliest positive increasing sequence with no 5-term subsequence of constant third differences.
%C A240557 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?
%C A240557 See crossreferences for sequences avoiding arithmetic progressions. - _M. F. Hasler_, Jan 12 2016
%t A240557 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
%o A240557 (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
%Y A240557 Cf. A240556 (starting with 0).
%Y A240557 No 3-term AP: A005836 (>=0), A003278 (>0);
%Y A240557 no 4-term AP: A240075 (>=0), A240555 (>0);
%Y A240557 no 5-term AP: A020654 (>=0), A020655 (>0);
%Y A240557 no 6-term AP: A020656 (>=0), A005838 (>0);
%Y A240557 no 7-term AP: A020657 (>=0), A020658 (>0);
%Y A240557 no 8-term AP: A020659 (>=0), A020660 (>0);
%Y A240557 no 9-term AP: A020661 (>=0), A020662 (>0);
%Y A240557 no 10-term AP: A020663 (>=0), A020664 (>0).
%Y A240557 Cf. A240075 and A240555 for sequences avoiding 4-term subsequences with constant second differences.
%K A240557 nonn
%O A240557 1,2
%A A240557 _T. D. Noe_, Apr 09 2014
%E A240557 Definition corrected by _M. F. Hasler_, Jan 12 2016