On the Sum of Corresponding Factorials and Triangular Numbers: Some Preliminary Results

Romer Castillo
2015 Asia Pacific Journal of Multidisciplinary Research   unpublished
A new sequence of natural numbers can be formed by adding corresponding factorials and triangular numbers. In this paper, such numbers were named factoriangular numbers. Mathematical experimentations on these numbers resulted to the establishment of some of its characteristics. These include the parity, compositeness, the number and sum of its positive divisors, abundancy and deficiency, Zeckendorf's decomposition, end digits, and digital roots of factoriangular numbers. Several theorems and
more » ... ollaries were proven and some conjectures were also presented.