A266728 Stanley sequence S_5(0,3).

0, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 25, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 50, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 71, 75, 78, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94, 96, 125, 128, 129, 130

Offset

0,2

Comments

Lexicographic first increasing sequence with a(0) = 0, a(1) = 3 and for all n > 1, {a(0), ..., a(n)} does not contain 5 terms in arithmetic progression.

Links

Table of n, a(n) for n=0..67.

R. A. Moy and D. Rolnick, Novel structures in Stanley sequences, Discrete Math., 339 (2016), 689-698. Also arXiv:1502.06013 [math.CO], 2015.

A. M. Odlyzko and R. P. Stanley, Some curious sequences constructed with the greedy algorithm, 1978.

Prog

(PARI) A266728(n, show=1, L=5, v=[0, 3], D=v->v[2..-1]-v[1..-2])={ 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]), #Set(D(vecextract(v, i)))>1||next(2), 2); break)); v[n+1]} \\ M. F. Hasler, Jan 18 2016

Crossrefs

Cf. A005836, A188053, A266727.

Cf. A185256 = S_3(0,3) = S(0,3), A267650 = S_4(0,3).

Sequence in context: A188040 A099352 A047207 * A039132 A187970 A122488

Adjacent sequences: A266725 A266726 A266727 * A266729 A266730 A266731

Keyword

nonn

Author

N. J. A. Sloane, Jan 04 2016

Extensions

More terms from M. F. Hasler, Jan 18 2016

Status

approved