2024/05/10/bb-2-5-is-hard

[utterances-bot]

BB(2, 5) is Hard (Hydra) | sligocki

Consider the Collatz-like function:

https://www.sligocki.com//2024/05/10/bb-2-5-is-hard.html

[sligocki]

Some OEIS sequences of interest:

• Sequence of values of "a": https://oeis.org/A061418
• Sequence of parties of it: https://oeis.org/A356556

[LegionMammal978]

Note that we can also define B₀(a, b) = B(a − 1, b), giving Start → B₀(2, 0); B₀(2n, b) → B₀(3n, b + 2); B₀(2n + 1, b) → B₀(3n + 2, b − 1). The a values can be expressed by a(0) = 2, a(n + 1) = ⌈3/2·a(n)⌉, yielding the sequence A061419 and the parity sequence A205083. This variation has much literature of its own surrounding it, but definite results (as opposed to heuristic results) are very elusive.

[bostick]

I prefer to think of f as f(n)=⌊3n/2⌋.

[nickdrozd]

Has there been any further analysis of Pavel's 2/5 champ? Especially, is anyone able to run it in a reasonable number of simulator steps?