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(PARI) A240075(n, show=0, L=4, o=2, v=[0], 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

For the analog sequence which avoids 5-term subsequences of constant third differences, see A240556 (>=0) and A240557 (>0).

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Definition corrected by N. J. A. Sloane, and _M. F. Hasler_, Jan 04 2016.

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Cf. A005836 (no 3-term starting at 0), A003278 (no 3-term starting at 1).

Cf. A240556, A240557.

Summary of increasing sequences avoiding arithmetic progressions of specified lengths (the second of each pair is obtained by adding 1 to the first):

3-term AP: A005836 (>=0), A003278 (>0);

4-term AP: A005839 (>=0), A005837 (>0);

5-term AP: A020654 (>=0), A020655 (>0);

6-term AP: A020656 (>=0), A005838 (>0);

7-term AP: A020657 (>=0), A020658 (>0);

8-term AP: A020659 (>=0), A020660 (>0);

9-term AP: A020661 (>=0), A020662 (>0);

10-term AP: A020663 (>=0), A020664 (>0).

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Earliest Lexicographically earliest nonnegative increasing sequence with such that no 4-term arithmetic progressionsfour terms have constant second differences.

For the positive sequence, see A240555, which is this sequence plus 1. Is there a simple way of determining this sequence, as in the case of the no 3-term arithmetic progression?

For the positive sequence, see A240555, which is this sequence plus 1.

Cf. A240556 (no 5-term starting at 0), A240557 (no 5-term starting at 1).

Cf. A240556, A240557.

Definition corrected by N. J. A. Sloane, Jan 04 2016.

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Vincenzo Librandi and T. D. Noe, <a href="/A240075/b240075_1.txt">Table of n, a(n) for n = 1..755</a> (first 123 terms from Vincenzo Librandi)

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