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%I #11 Dec 05 2025 18:23:24
%S 5,1,5,2,0,4,8,3,3,4,1,9
%N Decimal expansion of an observed ratio describing the separation of level sets in Collatz orbits.
%C See Sigg link for more information. The constant depends on the validity of the Collatz conjecture and on the persistence of the observed cluster pattern in all level sets of the Collatz tree.
%H Hugo Pfoertner, <a href="/A391017/a391017_1.txt">Table of n, A391017(n), A391018(n) and product</a>, (2025)
%H Markus Sigg, <a href="https://arxiv.org/abs/2012.07839">On the cluster structures in Collatz level sets</a>, arXiv:2012.07839 [math.GM], 2020.
%e 0.5152048334...
%o (PARI) \\ writes improved approximations
%o my(smin=1); forstep(n=1, oo, 2, my(k=n, s=1); while(k>1, if(k%6==4, s*=(k-1)/k); k=if(k%2, 3*k+1, k>>1)); if(s<smin, printf("%d %18.15f \n", n, s); smin=s))
%Y Cf. A127824, A391017, A391018.
%K nonn,cons,more
%O 0,1
%A _Hugo Pfoertner_ and _Markus Sigg_, Nov 25 2025