Geodesic
Collatz hypothesis and Planck's black body radiation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 3, pp. 408-414 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Collatz conjecture is considered and the density of values is compared to Planck's black body radiation, showing a remarkable agreement with each other. We also briefly discuss a generalisation of Collatz conjecture.
Keywords: black body radiation
Mots-clés : Collatz conjecture, Collatz conjecture generalisation. 
@article{JSFU_2024_17_3_a11,
     author = {Nicola Fabiano and Nikola Mirkov and Stojan Radenovi\'c},
     title = {Collatz hypothesis and {Planck's} black body radiation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {408--414},
     year = {2024},
     volume = {17},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2024_17_3_a11/}
}
TY  - JOUR
AU  - Nicola Fabiano
AU  - Nikola Mirkov
AU  - Stojan Radenović
TI  - Collatz hypothesis and Planck's black body radiation
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2024
SP  - 408
EP  - 414
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JSFU_2024_17_3_a11/
LA  - en
ID  - JSFU_2024_17_3_a11
ER  - 
%0 Journal Article
%A Nicola Fabiano
%A Nikola Mirkov
%A Stojan Radenović
%T Collatz hypothesis and Planck's black body radiation
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2024
%P 408-414
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/JSFU_2024_17_3_a11/
%G en
%F JSFU_2024_17_3_a11
Nicola Fabiano; Nikola Mirkov; Stojan Radenović. Collatz hypothesis and Planck's black body radiation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 3, pp. 408-414. http://geodesic.mathdoc.fr/item/JSFU_2024_17_3_a11/

[1] https://mathshistory.st-andrews.ac.uk/Biographies/Collatz

[2] D.Applegate, J.C.Lagarias, “Density Bounds for the $3x+1$ Problem 1. Tree-Search Method”, Math. Comput., 64 (1995), 411–426 | MR | Zbl

[3] D.Applegate, J.C.Lagarias, “Density Bounds for the $3x+1$ Problem 2. Krasikov Inequalities”, Math. Comput., 64 (1995), 427–438 | MR | Zbl

[4] R.K.Guy, “Collatz's Sequence”, Unsolved Problems in Number Theory, §E16, 2nd ed., Springer-Verlag, New York, 1994, 215–218 | MR

[5] S.A.Kurtz, J.Simon, “The Undecidability of the Generalized Collatz Problem”, Theory and Applications of Models of Computation, TAMC 2007, Proceedings of the 4th International Conference (Shanghai, May 22–25, 2007), eds. J.-Y. Cai, S. B. Cooper, and H. Zhu, Springer, Berlin, 2007, 542–553 | DOI | MR | Zbl

[6] https://mathworld.wolfram.com/CollatzProblem.htm

[7] M.Planck, “Über das Gesetz der Energieverteilung im Normalspektrum”, Annalen der Physik, 4(190):3 (1002), 553–563 | DOI