A267301 - OEIS

%I #6 Jan 13 2016 00:08:47

%S 1,2,3,4,6,7,8,9,12,14,17,20,21,23,25,31,32,37,46,47,53,56,61,63,64,

%T 67,70,72,76,87,90,93,104,112,116,120,135,138,146,153,164,177,179,180,

%U 197,201,221,224,276,277,279,282,283,285,287,295,305,317,320,327,340,354,361,364,377,380,385,391,403,415,424,430,443

%N Earliest positive increasing sequence having no 5-term subsequence with constant second differences.

%o (PARI) A267301(n, show=0, L=5, 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. A267300 (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. 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