A267304 Earliest nonnegative increasing sequence having no 7-term subsequence with constant second differences.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 26, 28, 29, 31, 33, 35, 38, 40, 41, 43, 49, 50, 52, 53, 58, 59, 62, 63, 64, 69, 70, 72, 73, 77, 81, 82

Offset: 1

Author

M. F. Hasler, Jan 12 2016

Keywords

• nonn
• more

Crossrefs

Cf. A267305 (positive variant: starting with 1).

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

Programs

PARI

A267304(n, show=0, L=7, o=2, v=[0], 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