A337025 Number of n-state 2-symbol halt-free Turing machines.

1, 16, 4096, 2985984, 4294967296, 10240000000000, 36520347436056576, 182059119829942534144, 1208925819614629174706176, 10314424798490535546171949056, 109951162777600000000000000000000, 1432052311740255546466984939315265536

Offset

0,2

Comments

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.

Links

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

Scott Aaronson, The Busy Beaver Frontier.

Nick Drozd, Beeping Busy Beavers.

Formula

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

Prog

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

Crossrefs

Cf. A052200.

Sequence in context: A016936 A321242 A013721 * A053859 A053863 A053765

Adjacent sequences: A337022 A337023 A337024 * A337026 A337027 A337028

Keyword

nonn,easy

Author

Nicholas Drozd, Aug 11 2020

Status

approved