lean_workbook_plus_42290

Let $2^k \equiv r_k \pmod{25}$ for $k\geq 0$ . The sequence $(r_k)_{k\geq 0}$ starts $1,2,4,8,16,7,\ldots$ and is periodic with period length $20$ , missing just the values $5,10,15,20$ among the integers from $1$ to $24$ . Therefore $s = \sum_{k=0}^{19} r_k = \sum_{\ell=1}^{24} \ell - (5+10+15+20) = 250$ .