Radó, T. On non-computable functions. (English) Zbl 1497.68176 Bell Syst. Tech. J. 41, 877-884 (1962). Summary: The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of non-negative integers has a largest element. Also, this principle is used only for sets which are exceptionally well-defined by current standards. No enumeration of computable functions is used, and in this sense the diagonal process is not employed. Thus, it appears that an apparently self-evident principle, of constant use in every area of mathematics, yields non-constructive entities. Cited in 1 ReviewCited in 34 Documents MSC: 68Q04 Classical models of computation (Turing machines, etc.) 03D10 Turing machines and related notions PDFBibTeX XMLCite \textit{T. Radó}, Bell Syst. Tech. J. 41, 877--884 (1962; Zbl 1497.68176) Full Text: DOI Online Encyclopedia of Integer Sequences: Busy Beaver sequence, or Rado’s sigma function: maximal number of 1’s that an n-state Turing machine can print on an initially blank tape before halting. Busy Beaver problem: a(n) = maximal number of steps that an n-state Turing machine can make on an initially blank tape before eventually halting. Largest value held in any register at the end of a halting computation by an n-instruction register Minski machine. Concatenated and flattened output distributions of the Turing machines described in the comments lines. Number of Turing machines with n states following the standard formalism of the busy beaver problem where the head of a Turing machine either moves to the right or to the left, but none once halted.