

A267304


Earliest nonnegative increasing sequence having no 7term subsequence with constant second differences.


4



0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 26, 28, 29, 31, 33, 35, 38, 40, 41, 43, 49, 50, 52, 53, 58, 59, 62, 63, 64, 69, 70, 72, 73, 77, 81, 82
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OFFSET

1,3


LINKS

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


PROG

(PARI) A267304(n, show=0, L=7, 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)>1next(2), 2); break)); v[#v]} \\ M. F. Hasler, Jan 12 2016


CROSSREFS

Cf. A267305 (positive variant: starting with 1).
No 3term AP: A005836 (>=0), A003278 (>0);
no 4term AP: A240075 (>=0), A240555 (>0);
no 5term AP: A020654 (>=0), A020655 (>0);
no 6term AP: A020656 (>=0), A005838 (>0);
no 7term AP: A020657 (>=0), A020658 (>0);
no 8term AP: A020659 (>=0), A020660 (>0);
no 9term AP: A020661 (>=0), A020662 (>0);
no 10term AP: A020663 (>=0), A020664 (>0).
Cf. A240075 and A240555 for sequences avoiding 4term subsequences with constant second differences.
Cf. A267300 and A267301 for sequences avoiding 5term subsequences with constant second differences.
Cf. A267302 and A267303 for sequences avoiding 6term subsequences with constant second differences.
Cf. A240556 and A240557 for sequences avoiding 5term subsequences with constant third differences.
Sequence in context: A057907 A109234 A335137 * A002855 A303234 A175233
Adjacent sequences: A267301 A267302 A267303 * A267305 A267306 A267307


KEYWORD

nonn,more


AUTHOR

M. F. Hasler, Jan 12 2016


STATUS

approved



