A267303 Earliest positive increasing sequence having no 6-term subsequence with constant second differences.

1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 18, 20, 21, 22, 25, 26, 28, 35, 36, 39, 41, 43, 46, 47, 49, 54, 55, 56, 64, 68, 74, 75, 81, 83, 84, 85, 87, 88, 90, 91, 93, 95, 103, 108, 109, 111, 118, 129, 134, 137, 140, 144, 145, 150, 151, 152, 153

Offset: 1

Author

M. F. Hasler, Jan 12 2016

Keywords

• nonn

Crossrefs

Cf. A267302 (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. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.

Programs

PARI

A267303(n, show=0, L=6, o=2, 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