Triangular number AND sum of first m factorials

01092018, 04:31 PM
Post: #1




Triangular number AND sum of first m factorials
153 (my favorite number) is both a triangular number (the sum of the integers 1 through \(n\); in this case \(n=17\)) as well as the sum of the factorials \(1!\) through \(m!\) (in this case \(m=5\)).
The first three natural numbers which have both of those properties are 1, 3 (both trivial) and 153. Find the next number in this sequence. For extra credit, find the mathematical relationship between \(n\) and \(m\) for all members of this sequence (which apparently is not yet in OEIS). <0ΙΈ0> Joe 

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