A267305 Earliest positive increasing sequence having no 7-term subsequence with constant second differences.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 25, 27, 29, 30, 32, 34, 36, 39, 41, 42, 44, 50, 51, 53, 54, 59, 60, 63, 64, 65, 70, 71, 73, 74, 78, 82, 83

Offset

1,2

Links

Table of n, a(n) for n=1..46.

Prog

(PARI) A267305(n, show=0, L=7, o=2, 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. A267304 (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. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.

Sequence in context: A043092 A023801 A332107 * A302478 A356939 A113619

Adjacent sequences: A267302 A267303 A267304 * A267306 A267307 A267308

Keyword

nonn,more

Author

M. F. Hasler, Jan 12 2016

Status

approved