A267302 Earliest nonnegative increasing sequence having no 6-term subsequence with constant second differences.

0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 19, 20, 21, 24, 25, 27, 34, 35, 38, 40, 42, 45, 46, 48, 53, 54, 55, 63, 67, 73, 74, 80, 82, 83, 84, 86, 87, 89, 90, 92, 94, 102, 107, 108, 110, 117, 128, 133, 136, 139, 143, 144, 149, 150, 151, 152

Offset

1,3

Links

Table of n, a(n) for n=1..60.

Prog

(PARI) A267302(n, show=0, L=6, 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

Cf. A267303 (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. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.

Sequence in context: A031942 A043090 A317044 * A023799 A267306 A001959

Adjacent sequences: A267299 A267300 A267301 * A267303 A267304 A267305

Keyword

nonn

Author

M. F. Hasler, Jan 12 2016

Status

approved