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

allocated for M. F. Hasler

Earliest positive increasing sequence with no 6-term subsequence of 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

1,2

(PARI) A267303(n, show=0, L=6, 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

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.

allocated

nonn,changed

M. F. Hasler, Jan 12 2016

approved

editing

allocated for M. F. Hasler

allocated

approved