On the existence of cycles of given length in integer sequences like x n + 1 = x n / 2 if x n even, and x n + 1 = 3 ⁢ x n + 1

Corrado Böhm; Giovanna Sontacchi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1978)

  • Volume: 64, Issue: 3, page 260-264
  • ISSN: 0392-7881

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Böhm, Corrado, and Sontacchi, Giovanna. "On the existence of cycles of given length in integer sequences like $x_{n+1} = x_{n}/2$ if $x_{n}$ even, and $x_{n+1} = 3 x_{n} + 1$." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 64.3 (1978): 260-264. <http://eudml.org/doc/290184>.

@article{Böhm1978,
author = {Böhm, Corrado, Sontacchi, Giovanna},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {3},
number = {3},
pages = {260-264},
publisher = {Accademia Nazionale dei Lincei},
title = {On the existence of cycles of given length in integer sequences like $x_\{n+1\} = x_\{n\}/2$ if $x_\{n\}$ even, and $x_\{n+1\} = 3 x_\{n\} + 1$},
url = {http://eudml.org/doc/290184},
volume = {64},
year = {1978},
}

TY - JOUR
AU - Böhm, Corrado
AU - Sontacchi, Giovanna
TI - On the existence of cycles of given length in integer sequences like $x_{n+1} = x_{n}/2$ if $x_{n}$ even, and $x_{n+1} = 3 x_{n} + 1$
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1978/3//
PB - Accademia Nazionale dei Lincei
VL - 64
IS - 3
SP - 260
EP - 264
LA - eng
UR - http://eudml.org/doc/290184
ER -

References

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  1. ADACI, N. - On Smia's Problem (in Japanese). 
  2. CONWAY, J. H. (1972) - Unpredictable iterations. Proceedings of the 1972 Number Theory Conference. University of Colorado. MR392904
  3. DUNN, R. (1973) - On Ulam's Problem. University of Colorado. Report CU-CS-011-73. 
  4. EVERETT, C. J. (1977) - Iteration of the Number-Theoretic Function f ⁢ ( 2 ⁢ n ) = n , f ⁢ ( 2 ⁢ n + 1 ) = 3 ⁢ n + 2 , «Advances in Matematics», 25. Los Alamos, New Mexico. Zbl0352.10001
  5. JACKSON, D. M. (1973) - Private communication. University of Waterloo. 
  6. ULAM, S. (1975) - Private communication. University of Colorado. 

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