Problem E

Missing the Fives III

Bobbi lists the positive integers, in order, excluding all multiples of \(5\). Her resulting list is \[1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, \ldots\] Determine the sum of the first \(2023\) integers in Bobbi’s list.

Note:

In solving this problem, it may be helpful to use the fact that the sum
of the first \(n\) positive integers is
equal to \(\tfrac{n(n+1)}{2}\). That
is, \[1 + 2 + 3 + \cdots + n =
\frac{n(n+1)}{2}\]