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A267303 Earliest positive increasing sequence having no 6-term subsequence with constant second differences. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..60.

PROG

(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

CROSSREFS

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.

Sequence in context: A184486 A047203 A080919 * A267307 A032974 A127565

Adjacent sequences:  A267300 A267301 A267302 * A267304 A267305 A267306

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jan 12 2016

STATUS

approved

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Last modified January 20 16:46 EST 2019. Contains 319335 sequences. (Running on oeis4.)