0,2

A Turing machine is halt-free if none of its instructions lead to the halt state.

This sequence is strictly less than A052200(n) for all n > 0, since halt-free n-state machines are a strict subset of all n-state machines.

Solutions to the so-called "Beeping Busy Beaver" problem will almost certainly be halt-free programs.

Table of n, a(n) for n=0..11.

Scott Aaronson, The Busy Beaver Frontier.

Nick Drozd, Beeping Busy Beavers.

a(n) = ((4*n)^2)^n.

(Python) [((4 * n) ** 2) ** n for n in range(12)]

Cf. A052200.

Sequence in context: A016936 A321242 A013721 * A053859 A053863 A053765

Adjacent sequences: A337022 A337023 A337024 * A337026 A337027 A337028

nonn,easy

Nicholas Drozd, Aug 11 2020

approved