A386792 Antihydra, a BB(6) Turing machine (values of a).

8, 12, 18, 27, 40, 60, 90, 135, 202, 303, 454, 681, 1021, 1531, 2296, 3444, 5166, 7749, 11623, 17434, 26151, 39226, 58839, 88258, 132387, 198580, 297870, 446805, 670207, 1005310, 1507965, 2261947, 3392920, 5089380, 7634070, 11451105, 17176657, 25764985, 38647477

Offset

0,1

Comments

Let f(a, b) = (3*a / 2, b + 2) if a is even, otherwise ((3*a - 1)/2, b - 1). The Busy Beaver challenge is to find natural numbers n and v, such that after n iterations, starting with f(8, 0), the result is (v, -1).

We consider the sequence to be defined for all values of n, regardless of whether 'b' ever takes the value -1 or not. The sequence records the values of 'a' in this iteration. See A385902 for the values of 'b'.

Links

Paolo Xausa, Table of n, a(n) for n = 0..5000

The Busy Beaver Challenge, Antihydra.

The Busy Beaver Wiki, Antihydra.

Shawn Ligocki, BB(6) is Hard (Antihydra), July 2024.

Maple

aList := proc(halt) a := 8; u := 0; H := 8;
from 0 to halt do
    q, r := iquo(a, 2), irem(a, 2):
    a, u := a + q, u + r: H := H, a
od: H end: aList(37);

Mathematica

A386792List[n_] := Module[{next},
    next[{a_, u_}] := {a, u} + QuotientRemainder[a, 2];
    NestList[next, {8, 0}, n][[All, 1]]];
A386792List[38] (* Peter Luschny, Aug 05 2025 *)

Prog

(Python)
def A386792List(n) -> list[int]:
    (a, b), H = (8, 0), [8]
    for _ in range(n):
        a, b = map(sum, zip((a, b), divmod(a, 2)))
        H.append(a)
    return H
(PARI) a(m)=n=8; for(i=1, m, n=floor(3*n/2)); n \\ Ralf Stephan, Mar 09 2026

Crossrefs

Cf. A385902 (values of b), A028444, A060843, A061418 (starting with 2).

Sequence in context: A380168 A276403 A171241 * A120137 A274951 A364776

Adjacent sequences: A386789 A386790 A386791 * A386793 A386794 A386795

Keyword

nonn

Author

Peter Luschny, Aug 02 2025

Status

approved