Sequence of Integers Generated by Summing the Digits of their Squares

Objectives: To establish some properties of sequence of numbers generated by summing the digits of their respective squares. Methods/Analysis: Two distinct sequences were obtained, one is obtained from summing the digits of squared integers and the other is a sequence of numbers can never be obtained be obtained when integers are squared. Also some mathematical operations were applied to obtain some subsequences. The relationship between the sequences was established by using correlation, regression and analysis of variance. Findings: Multiples of 3 were found to have multiples of 9 even at higher powers when they are squared and their digits are summed up. Other forms are patternless, sequences notwithstanding. The additive, divisibility, multiplicative and uniqueness properties of the two sequences yielded some unique subsequences. The closed forms and the convergence of the ratio of the sequences were obtained. Strong positive correlation exists between the two sequences as they can be used to predict each other. Analysis of variance showed that the two sequences are from the same distribution. Conclusion/Improvement: The sequence generated by summing the digits of squared integers can be known as Covenant numbers. More research is needed to discover more properties of the sequences.