OEIS sequence A272573 describes a sequence generated in the following way:

Start a spiral of numbers on a hexagonal tiling, with the initial hexagon as a(1) = 1. a(n) is the smallest positive integer not equal to or previously adjacent to its neighbors.


The sequence begins 1,2,3,4,5,6,7,4,6,8,....

If you look at the scatterplot, there appears to be a very sparse region. Scatterplot, A272573


I'm curious if there is some heuristic which explains why this gap appears. (In particular, the heuristic should also account for the fact that such a gap does not appear in A260643, the analogous sequence on a square grid.)

  • $\begingroup$ Very interesting. Did you use the ruby code from OEIS (which I can't read) or a program in some other language? If the latter, would you post it? $\endgroup$ – saulspatz Dec 12 '18 at 3:16
  • $\begingroup$ Here's a post on Code Golf Stack Exchange with two other programs that corroborate the Ruby program. The code there is (deliberately) hard to read, but they have explanations. $\endgroup$ – Peter Kagey Dec 14 '18 at 19:40
  • $\begingroup$ Thanks. I hate code golf as a general rule (possibly because I'm no good at it), but I'll take a look. $\endgroup$ – saulspatz Dec 14 '18 at 19:51
  • $\begingroup$ Each cell has 6 neighbors and 12 level 2 neighbors, so how can its value be more than 19? Why the scatter plot looks unbounded? What am I missing? $\endgroup$ – Todor Markov Dec 16 '18 at 10:02
  • 2
    $\begingroup$ @TodorMarkov: I think "equal to or previously adjacent to its neighbors" means "equal to or previously adjacent to a cell with the same value as a neighboring cell". $\endgroup$ – mjqxxxx Dec 16 '18 at 15:28

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