This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006997 M0185 #43 Apr 09 2025 14:14:57 %S A006997 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, %T A006997 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, %U A006997 5,6,6,7,4,5,5,4,5,5,6,6,7,0,0,1,0,0,1 %N A006997 Partitioning integers to avoid arithmetic progressions of length 3. %C A006997 a(n) = 0 iff n in A005836. %D A006997 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006997 Ben Chen, Richard Chen, Joshua Guo, Tanya Khovanova, Shane Lee, Neil Malur, Nastia Polina, Poonam Sahoo, Anuj Sakarda, Nathan Sheffield, and Armaan Tipirneni, <a href="https://arxiv.org/abs/1808.04304">On Base 3/2 and its sequences</a>, arXiv:1808.04304 [math.NT], 2018. %H A006997 Joseph Gerver, James Propp and Jamie Simpson, <a href="http://dx.doi.org/10.1090/S0002-9939-1988-0929018-1">Greedily partitioning the natural numbers into sets free of arithmetic progressions</a> Proc. Amer. Math. Soc. 102 (1988), no. 3, 765-772. %H A006997 A. M. Odlyzko and R. P. Stanley, <a href="https://math.mit.edu/~rstan/papers/od.pdf">Some curious sequences constructed with the greedy algorithm</a>, 1978. %H A006997 James Propp and N. J. A. Sloane, <a href="/A006997/a006997.pdf">Email, March 1994</a> %H A006997 J. Shallit, <a href="https://cs.uwaterloo.ca/~shallit/Talks/kreg7.pdf">k-regular Sequences</a> %H A006997 J. Shallit, <a href="https://cs.uwaterloo.ca/~shallit/Papers/ntfl.pdf">Number theory and formal languages</a>, 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. %F A006997 a(3n+k) = floor((3*a(n)+k)/2), 0 <= k <= 2. %F A006997 a(n) = A100480(n+1) - 1. - _Pontus von Brömssen_, Apr 09 2025 %Y A006997 Cf. A005836, A100480. %K A006997 nonn,easy %O A006997 0,8 %A A006997 _N. J. A. Sloane_, _James Propp_