A267307 Earliest positive increasing sequence having no 6-term subsequence with constant third differences.

1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 29, 30, 32, 33, 34, 35, 36, 38, 39, 41, 48, 80, 94, 95, 97, 98, 99, 100, 101, 103, 104, 106, 111, 117, 123, 129, 131, 141, 149, 267, 282, 297, 304, 305, 307, 309, 312, 314, 319, 325, 327, 328, 329, 331, 332, 333, 338

Offset: 1

Author

M. F. Hasler, Jan 12 2016

Keywords

• nonn

Crossrefs

Cf. A267306 (nonnegative variant: 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.

Cf. A267300 and A267301 for sequences avoiding 5-term subsequences with constant second differences.

Cf. A267302 and A267303 for sequences avoiding 6-term subsequences with constant second differences.

Cf. A267304 and A267305 for sequences avoiding 7-term subsequences with constant second differences.

Cf. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.

Programs

PARI

A267307(n, show=0, L=6, 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

More terms from Jinyuan Wang, Jan 08 2021