A006997 Partitioning integers to avoid arithmetic progressions of length 3. (Formerly M0185)

0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 4, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 4, 3, 3, 4, 1, 2, 2, 3, 3, 4, 3, 3, 4, 4, 5, 5, 4, 5, 5, 6, 6, 7

Offset

0,8

Comments

a(n) = 0 iff n in A005836.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..71.

B. Chen, R. Chen, J. Guo, S. Lee et al, On Base 3/2 and its sequences, arXiv:1808.04304 [math.NT], 2018.

Joseph Gerver, James Propp and Jamie Simpson, Greedily partitioning the natural numbers into sets free of arithmetic progressions Proc. Amer. Math. Soc. 102 (1988), no. 3, 765-772.

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

James Propp and N. J. A. Sloane, Email, March 1994

J. Shallit, k-regular Sequences

J. Shallit, Number theory and formal languages, in D. A. Hejhal, J. Friedman, M. C. Gutzwiller and A. M. Odlyzko, eds., Emerging Applications of Number Theory, IMA Volumes in Mathematics and Its Applications, V. 109, Springer-Verlag, 1999, pp. 547-570.

Formula

a(3n+k) = floor((3*a(n)+k)/2), 0 <= k <= 2.

Crossrefs

Sequence in context: A032337 A058190 A055736 * A141612 A316342 A297814

Adjacent sequences: A006994 A006995 A006996 * A006998 A006999 A007000

Keyword

nonn,easy

Author

N. J. A. Sloane, James Propp

Status

approved