Paper Abstract and Keywords |
Presentation |
2021-12-03 16:00
Lower bounds for the total stopping time of 3x+ 1iterates revisited Kazuyuki Amano (Gunma Univ.) COMP2021-29 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Let $T: mathbb{N} rightarrow mathbb{N}$ be the $3x+1$ function defined by
$T(n) = n/2$ if $n$ is even and $T(n) = (3n+1)/2$ if $n$ is odd.
Let $sigma_infty(n)$ be the minimal $k$ such that $T^{(k)}(n)=1$ if one exists and $+ infty$ otherwise.
By extending the computational efforts by Applegate and Lagarias (Math. Comp., 2003),
we show that $sigma_infty(n) geq (frac{1}{2} ln frac{4}{3})^{-1} ln n approx 6.9521 ln n$ for infinitely many $n$, improving the former bound of $sigma_infty(n) > 6.1413 ln n$.
The certificate of our proof consists of $19,065,883,794$ critical paths each for a different $3x+1$ tree of max-depth 74. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
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Reference Info. |
IEICE Tech. Rep., vol. 121, no. 285, COMP2021-29, pp. 40-43, Dec. 2021. |
Paper # |
COMP2021-29 |
Date of Issue |
2021-11-26 (COMP) |
ISSN |
Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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COMP2021-29 |
Conference Information |
Committee |
COMP |
Conference Date |
2021-12-03 - 2021-12-03 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Kanazawa Chamber of Commerce and Industry |
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(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2021-12-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
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(See Japanese page) |
Title (in English) |
Lower bounds for the total stopping time of 3x+ 1iterates revisited |
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Kazuyuki Amano |
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Gunma University (Gunma Univ.) |
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Speaker |
Author-1 |
Date Time |
2021-12-03 16:00:00 |
Presentation Time |
20 minutes |
Registration for |
COMP |
Paper # |
COMP2021-29 |
Volume (vol) |
vol.121 |
Number (no) |
no.285 |
Page |
pp.40-43 |
#Pages |
4 |
Date of Issue |
2021-11-26 (COMP) |
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