Doubly Consecutive Sums

Answer: $201$


Sum of 2 consecutive numbers is $n + (n+1)=2n+1$
Sum of 5 consecutive numbers is $m + (m+1)+(m+2)+(m+3)+(m+4) = 5m+10$
($m$ and $n$ different numbers because the sums have different starting points)

$2n+1=5m+10$

Can find $n$ from any $m$, as long as $5m+10$ is odd
$5m+10$ is odd whenever $m$ is odd
And $5m+10 \lt 2017$
       $\therefore 5m \lt 2007\\ \therefore m \le 401$

There are $201$ odd numbers up to $401$