Research On Integer Sequence Learning Method

Integer sequence learning(ISL)refers to the discovery of the rule of integer sequence by using the front n terms of an integer sequence.The research of integer sequence has promoted the development of number theory.Integer sequences have been widely used in many fields and their research has important significance.In this paper,the research of ISL method is carried out,and two kinds of ISL methods are proposed,which are the pattern-based integer sequence learning method and the multi-strategy based integer sequence learning method.The pattern-based ISL method(formula method)uses the formula to represent the rule of sequence.This method formulates the formula model for formula discovery.The formula model includes the recursive mode,the polynomial and the exponential combination mode and the residual mode.The formula method includes three steps,namely pattern recognition,formula solving,and formula verification.The method first builds the rule base,and then uses the rules for pattern recognition.Finally,it solves and verifies the formula by using the solution algorithm of each pattern.The solution algorithm is developed by analyzing the pattern features of each pattern.The results are as follows: the accuracy rate is 94.522%,the recall rate is 19.053%,and the F value is 31.713%.ISL method based on multi-strategy combines three methods to predict the integer sequence,which are the formula method,the correlation method and the neural network method.The correlation method uses the relation between the sequences to represent the integer sequence.In order to quickly find the correlated instances in the instance library,a correlation method of "characterization-finding correlation instance-relational solution" is proposed.The neural network method uses the model to predict the follow-up values of the sequence.By analyzing the characteristics of integer sequence,we choose recurrent neural network to build a series prediction model.The ISL method based on multi-strategy achieves good results of F value 41.597%,accuracy rate 59.574% and recall rate 31.951%.Finally,the formula discovery system FDS is developed.The system realizes the formula method and correlation method.Including the formula solving and relationship solving two parts,it can be used for integer sequence learning and application in various fields.For example,chemistry,medicine and other fields.In addition,the system has an auxiliary role in the development of intellectual games.