A391016 Decimal expansion of an observed ratio describing the separation of level sets in Collatz orbits.

5, 1, 5, 2, 0, 4, 8, 3, 3, 4, 1, 9

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..11.

Hugo Pfoertner, Table of n, A391017(n), A391018(n) and product, (2025)

Markus Sigg, On the cluster structures in Collatz level sets, arXiv:2012.07839 [math.GM], 2020.

Example

0.5152048334...

Prog

(PARI) \\ writes improved approximations
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))

Crossrefs

Cf. A127824, A391017, A391018.

Sequence in context: A388123 A264483 A050340 * A021955 A055191 A381526

Adjacent sequences: A391013 A391014 A391015 * A391017 A391018 A391019

Keyword

nonn,cons,more

Author

Hugo Pfoertner and Markus Sigg, Nov 25 2025

Status

approved