[seqfan] A prime-like example?

[brad klee]

Re: http://list.seqfan.eu/pipermail/seqfan/2023-May/074580.html

Item 5 could be helped by a list of what those "similar properties" should be.
My understanding is limited, but here's a few that I've seen:

→ Monotonic increasing
→ Arbitrarily large gaps→ Always a prime between n and 2*n
→ n/log(n) asymptotics
→ Probably computationally irreducible

Recently we've discovered a Cellular Automaton conjectured to show some
of these properties, and it also can have a Gilbreath transform which
alternates 1's and 0's. The definitions are here:

https://community.wolfram.com/groups/-/m/t/2918701

To repeat speculation, perhaps the constant 1's sequence should be seen
as a sign of perfection, with the alternation between two values indicating
something akin to broken symmetry.

All the best,

--Brad