- 期刊
Collatz Total Stopping Times with Neural Networks
摘要
The Collatz conjecture, or the 3n+1 conjecture, is an open problem in mathematics which is defined as follows: the sequence (which is called the Collatz sequence with respect to the starting value a_0) {a_n|n≥0} satisfies a_n=3a_(n-1)+1 if a_(n-1) is odd and a_n=a_(n-1)/2 otherwise eventually goes to 1 regardless the starting value a_0. We call the smallest n such that a_n=1 the total stopping time of the sequence with respect to a_0. For example, the sequence a_0=7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1 has a total stopping time of 16. This paper explores a neural network approach to approximate total stopping times in the Collatz conjecture. As of now, the model is unable to predict Collatz stopping times with good accuracy. However, this paper sheds light on a new method with which this problem can be experimented on.