7
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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.

A272573

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

Question

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.)

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  • $\begingroup$ 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
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    $\begingroup$ @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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