cp's OEIS Frontend

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

%I A386792 #30 Aug 05 2025 06:26:45
%S A386792 8,12,18,27,40,60,90,135,202,303,454,681,1021,1531,2296,3444,5166,
%T A386792 7749,11623,17434,26151,39226,58839,88258,132387,198580,297870,446805,
%U A386792 670207,1005310,1507965,2261947,3392920,5089380,7634070,11451105,17176657,25764985,38647477
%N A386792 Antihydra, a BB(6) Turing machine (values of a).
%C A386792 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).
%C A386792 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'.
%H A386792 Paolo Xausa, <a href="/A386792/b386792.txt">Table of n, a(n) for n = 0..5000</a>
%H A386792 The Busy Beaver Challenge, <a href="https://wiki.bbchallenge.org/wiki/Antihydra">Antihydra</a>.
%H A386792 The Busy Beaver Wiki, <a href="https://bbchallenge.org/antihydra">Antihydra</a>.
%H A386792 Shawn Ligocki, <a href="https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html">BB(6) is Hard (Antihydra)</a>, July 2024.
%p A386792 aList := proc(halt) a := 8; u := 0; H := 8;
%p A386792 from 0 to halt do
%p A386792     q, r := iquo(a, 2), irem(a, 2):
%p A386792     a, u := a + q, u + r: H := H,a
%p A386792 od: H end: aList(37);
%t A386792 A386792List[n_] := Module[{next},
%t A386792     next[{a_, u_}] := {a, u} + QuotientRemainder[a, 2];
%t A386792     NestList[next, {8, 0}, n][[All, 1]]];
%t A386792 A386792List[38] (* _Peter Luschny_, Aug 05 2025 *)
%o A386792 (Python)
%o A386792 def A386792List(n) -> list[int]:
%o A386792     (a, b), H = (8, 0), [8]
%o A386792     for _ in range(n):
%o A386792         a, b = map(sum, zip((a, b), divmod(a, 2)))
%o A386792         H.append(a)
%o A386792     return H
%Y A386792 Cf. A385902 (values of b), A028444, A060843.
%K A386792 nonn
%O A386792 0,1
%A A386792 _Peter Luschny_, Aug 02 2025