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%I #4 Jan 13 2016 00:41:59
%S 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,
%T 46,47,49,54,55,56,64,68,74,75,81,83,84,85,87,88,90,91,93,95,103,108,
%U 109,111,118,129,134,137,140,144,145,150,151,152,153
%N Earliest positive increasing sequence having no 6-term subsequence with constant second differences.
%o (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
%Y Cf. A267302 (nonnegative variant: starting with 0).
%Y No 3-term AP: A005836 (>=0), A003278 (>0);
%Y no 4-term AP: A240075 (>=0), A240555 (>0);
%Y no 5-term AP: A020654 (>=0), A020655 (>0);
%Y no 6-term AP: A020656 (>=0), A005838 (>0);
%Y no 7-term AP: A020657 (>=0), A020658 (>0);
%Y no 8-term AP: A020659 (>=0), A020660 (>0);
%Y no 9-term AP: A020661 (>=0), A020662 (>0);
%Y no 10-term AP: A020663 (>=0), A020664 (>0).
%Y Cf. A240075 and A240555 for sequences avoiding 4-term subsequences with constant second differences.
%Y Cf. A267300 and A267301 for sequences avoiding 5-term subsequences with constant second differences.
%Y Cf. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.
%K nonn
%O 1,2
%A _M. F. Hasler_, Jan 12 2016
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