A385902 -id:A385902 - cp's OEIS frontend

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

Peter Luschny, Aug 02 2025

nonn

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'.

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.

Cf. A385902 (values of b), A028444, A060843.

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);

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 *)

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

cp's OEIS Frontend

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

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