A240075 Lexicographically earliest nonnegative increasing sequence such that no four terms have constant second differences.

0, 1, 2, 4, 5, 8, 15, 16, 17, 20, 44, 51, 52, 53, 56, 58, 64, 78, 166, 167, 192, 195, 196, 200, 202, 203, 206, 217, 226, 248, 249, 276, 312, 649, 657, 678, 681, 682, 715, 726, 740, 743, 747, 750, 771, 790, 830, 833, 836, 838, 842, 854, 875, 908, 911, 971

Offset

1,3

Links

Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 1..755 (first 123 terms from Vincenzo Librandi)

Mathematica

t = {0, 1, 2}; Do[s = Table[Append[i, n], {i, Subsets[t, {3}]}]; If[! MemberQ[Flatten[Table[Differences[i, 3], {i, s}]], 0], AppendTo[t, n]], {n, 3, 1000}]; t

Prog

(PARI) A240075(n, show=0, L=4, o=2, v=[0], 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

Crossrefs

For the positive sequence, see A240555, which is this sequence plus 1.

Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):

3-term AP: A005836 (>=0), A003278 (>0);

4-term AP: A005839 (>=0), A005837 (>0);

5-term AP: A020654 (>=0), A020655 (>0);

6-term AP: A020656 (>=0), A005838 (>0);

7-term AP: A020657 (>=0), A020658 (>0);

8-term AP: A020659 (>=0), A020660 (>0);

9-term AP: A020661 (>=0), A020662 (>0);

10-term AP: A020663 (>=0), A020664 (>0).

For the analog sequence which avoids 5-term subsequences of constant third differences, see A240556 (>=0) and A240557 (>0).

Sequence in context: A226791 A357177 A184775 * A272229 A229083 A194415

Adjacent sequences: A240072 A240073 A240074 * A240076 A240077 A240078

Keyword

nonn

Author

T. D. Noe, Apr 09 2014

Extensions

Definition corrected by N. J. A. Sloane and M. F. Hasler, Jan 04 2016.

Status

approved