Asymptotic growth of a non-computable sequence

[Kreinovich, Vladik]

Since a(n) has n binary digits, it is between 2^n and 2^{n+1} = 2*2^n, so this is a clear asymptotic

Maybe you meant something else?

From: FOM [mailto:fom-bounces at cs.nyu.edu] On Behalf Of José Manuel Rodríguez Caballero
Sent: Tuesday, August 10, 2021 11:01 PM
To: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: Asymptotic growth of a non-computable sequence

Dear FOM members,
  In a recent preprint [1] comparing 't Hooft's and Wolfram's deterministic models of quantum mechanics, I considered the following sequence: a(n) is the smallest number having n binary digits, which can't be compressed concerning a fixed Turing machine. I would appreciate some references to tools to estimate the asymptotic growth of this sequence.

Kind regards,
José M.

References:
[1] arXiv:2108.03751 [quant-ph]

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