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A Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of x2 over the Count of 3∗x+1 Is Larger than ln3ln2
المؤلف
المصدر
International Journal of Mathematics and Mathematical Sciences
العدد
المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-14، 14ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2020-08-25
دولة النشر
مصر
عدد الصفحات
14
التخصصات الرئيسية
الملخص EN
We propose reduced Collatz conjecture and prove that it is equivalent to Collatz conjecture but more primitive due to reduced dynamics.
We study reduced dynamics (that consists of occurred computations from any starting integer to the first integer less than it) because it is the component of original dynamics (from any starting integer to 1).
Reduced dynamics is denoted as a sequence of “I” that represents (3∗x+1)/2 and “O” that represents x/2.
Here, 3∗x+1 and x/2 are combined together because 3∗x+1 is always even and thus followed by x/2.
We discover and prove two key properties on reduced dynamics: (1) Reduced dynamics is invertible.
That is, given reduced dynamics, a residue class that presents such reduced dynamics can be computed directly by our derived formula.
(2) Reduced dynamics can be constructed algorithmically, instead of by computing concrete 3∗x+1 and x/2 step by step.
We discover the sufficient and necessary condition that guarantees a sequence consisting of “I” and “O” to be a reduced dynamics.
Counting from the beginning of a sequence, if and only if the count of x/2 over the count of 3∗x+1 is larger than ln3/ln2, reduced dynamics will be obtained (i.e., current integer will be less than starting integer).
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Ren, Wei. 2020. A Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of x2 over the Count of 3∗x+1 Is Larger than ln3ln2. International Journal of Mathematics and Mathematical Sciences،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1172667
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Ren, Wei. A Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of x2 over the Count of 3∗x+1 Is Larger than ln3ln2. International Journal of Mathematics and Mathematical Sciences No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1172667
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Ren, Wei. A Reduced Collatz Dynamics Maps to a Residue Class, and Its Count of x2 over the Count of 3∗x+1 Is Larger than ln3ln2. International Journal of Mathematics and Mathematical Sciences. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1172667
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1172667
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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