The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Untuk sebarang integer positif n, takrifkan fungsi berulang $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ genap, } 3n+1, & mbox{ $n$ ganjil. } end{array} ight.$ Andaikan k (sekiranya wujud) adalah nombor terendah sedemikian fk(n)<n, dan operasi "darab dengan 3 dan menambah satu" berlaku O(n) kali dan "bahagi dengan 2" berlaku E(n) kali dari n kepada fk(n). Kami menjangkakan bahawa 2E(n)-Sembilan-belas sembilan puluh lima<3O(n)<2E(n). Tekaan ini adalah serupa dengan sangkaan yang dicadangkan oleh Terras pada tahun 1976, dan kami juga memberikan batas atas untuk jangka baki n.
Yuyin YU
Guangzhou University,School of Mathematics and Information Science
Zongxiang YI
Guangzhou University
Chuanming TANG
Guangzhou University
Jian GAO
Shandong University of Technology
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Salinan
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
Salinan
@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},}
Salinan
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 -