Terras 1976 stopping time problem

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Riho Terras, A stopping time problem on the positive integers, Acta Arith. 30 (1976) 241-252 (ICM/matwbn digitized scan via EuDML doc 205476; two journal pages per sheet, no text layer).

Works with the shortcut map T = (3^X(n) n + X(n))/2, introduced here -- the map convention is pinned from this primary text. Proves the stopping time chi(n) possesses a well-defined limiting distribution F(k) = lim (1/m) mu{n <= m : chi(n) >= k} (Theorem 1.11) with F(k) -> 0 (Theorem 1.17): almost all n in natural density have finite stopping time, via the tau-stopping time (later called the coefficient stopping time) and the uniform distribution of parity vectors over residue classes mod 2^k. Relevance: The founding density result on problem 1135: almost all n in natural density have finite 3x+1 stopping time, with a limiting stopping-time distribution.

Source: PDF. The scan is image-only and its rendered first and last pages show no copyright or license line; the journal's record offers the PDF under the download link "Pobierz zgodnie z CC-BY", rendered "Free download under CC-BY license" on the English site, and names no version or URL for it (https://www.impan.pl/get/doi/10.4064/aa-30-3-241-252, read 2026-10-02): the Creative Commons Attribution license, with no version stated.

Bears on. #1135