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

1,2

Links

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

Prog

(PARI) A267307(n, show=0, L=6, o=3, v=[1], 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. 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.

Sequence in context: A047203 A080919 A267303 * A032974 A127565 A082186

Adjacent sequences: A267304 A267305 A267306 * A267308 A267309 A267310

Keyword

nonn

Author

M. F. Hasler, Jan 12 2016

Extensions

More terms from Jinyuan Wang, Jan 08 2021

Status

approved