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A267305 Earliest positive increasing sequence having no 7-term subsequence with constant second differences. 4
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 25, 27, 29, 30, 32, 34, 36, 39, 41, 42, 44, 50, 51, 53, 54, 59, 60, 63, 64, 65, 70, 71, 73, 74, 78, 82, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

PROG

(PARI) A267305(n, show=0, L=7, 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. A267304 (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. A267302 and A267303 for sequences avoiding 6-term subsequences with constant second differences.

Cf. A240556 and A240557 for sequences avoiding 5-term subsequences with constant third differences.

Sequence in context: A043092 A023801 A332107 * A302478 A113619 A325114

Adjacent sequences:  A267302 A267303 A267304 * A267306 A267307 A267308

KEYWORD

nonn,more

AUTHOR

M. F. Hasler, Jan 12 2016

STATUS

approved

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)