IEICE TRANSACTIONS on Fundamentals
On the Glide of the 3x+1 Problem
Summary :
For any positive integer n, define an iterated function $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ even, } 3n+1, & mbox{ $n$ odd. } end{array} ight.$ Suppose k (if it exists) is the lowest number such that fk(n)<n, and the operation of “multiplying by 3 and adding one” occurs O(n) times and that of “dividing by 2” occurs E(n) times from n to fk(n). We conjecture that 2E(n)-1<3O(n)<2E(n). This conjecture is similar to the conjecture proposed by Terras in 1976, and we also give an upper bound for the residual term of n.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.3 pp.613-615
- Publication Date
- 2019/03/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.613
- Type of Manuscript
- LETTER
- Category
- Mathematical Systems Science
Authors
Yuyin YU
Guangzhou University,School of Mathematics and Information Science
Zongxiang YI
Guangzhou University
Chuanming TANG
Guangzhou University
Jian GAO
Shandong University of Technology
Keyword
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Yuyin YU, Zongxiang YI, Chuanming TANG, Jian GAO, "On the Glide of the 3x+1 Problem" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 3, pp. 613-615, March 2019, doi: 10.1587/transfun.E102.A.613.
Abstract: For any positive integer n, define an iterated function $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ even, } 3n+1, & mbox{ $n$ odd. } end{array}
ight.$ Suppose k (if it exists) is the lowest number such that fk(n)<n, and the operation of “multiplying by 3 and adding one” occurs O(n) times and that of “dividing by 2” occurs E(n) times from n to fk(n). We conjecture that 2E(n)-1<3O(n)<2E(n). This conjecture is similar to the conjecture proposed by Terras in 1976, and we also give an upper bound for the residual term of n.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.613/_p
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@ARTICLE{e102-a_3_613,
author={Yuyin YU, Zongxiang YI, Chuanming TANG, Jian GAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Glide of the 3x+1 Problem},
year={2019},
volume={E102-A},
number={3},
pages={613-615},
abstract={For any positive integer n, define an iterated function $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ even, } 3n+1, & mbox{ $n$ odd. } end{array}
ight.$ Suppose k (if it exists) is the lowest number such that fk(n)<n, and the operation of “multiplying by 3 and adding one” occurs O(n) times and that of “dividing by 2” occurs E(n) times from n to fk(n). We conjecture that 2E(n)-1<3O(n)<2E(n). This conjecture is similar to the conjecture proposed by Terras in 1976, and we also give an upper bound for the residual term of n.},
keywords={},
doi={10.1587/transfun.E102.A.613},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - On the Glide of the 3x+1 Problem
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 613
EP - 615
AU - Yuyin YU
AU - Zongxiang YI
AU - Chuanming TANG
AU - Jian GAO
PY - 2019
DO - 10.1587/transfun.E102.A.613
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2019
AB - For any positive integer n, define an iterated function $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ even, } 3n+1, & mbox{ $n$ odd. } end{array}
ight.$ Suppose k (if it exists) is the lowest number such that fk(n)<n, and the operation of “multiplying by 3 and adding one” occurs O(n) times and that of “dividing by 2” occurs E(n) times from n to fk(n). We conjecture that 2E(n)-1<3O(n)<2E(n). This conjecture is similar to the conjecture proposed by Terras in 1976, and we also give an upper bound for the residual term of n.
ER -
English
