

A267306


Earliest nonnegative increasing sequence having no 6term subsequence with constant third differences.


2



0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 28, 29, 31, 32, 33, 34, 35, 37, 38, 40, 47, 79, 93, 94, 96, 97, 98, 99, 100, 102, 103, 105, 110, 116, 122, 128, 130, 140, 148, 266, 281, 296, 303, 304, 306, 308, 311, 313, 318, 324, 326, 327, 328, 330, 331, 332, 337
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OFFSET

1,3


LINKS

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


PROG

(PARI) A267306(n, show=0, L=6, o=3, 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. A267307 (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. A267304 and A267305 for sequences avoiding 7term subsequences with constant second differences.
Cf. A240556 and A240557 for sequences avoiding 5term subsequences with constant third differences.
Sequence in context: A317044 A267302 A023799 * A001959 A263135 A119930
Adjacent sequences: A267303 A267304 A267305 * A267307 A267308 A267309


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 12 2016


EXTENSIONS

More terms from Jinyuan Wang, Jan 01 2021


STATUS

approved



