wat an intersting sequence

This sequence is a "reverse AP sum" sequence. If $i_n^{th}$ is the last of term $a_j = n$ , then $i_n = \dfrac {n(n+1)}{2}$ . For example: $i_1 = \frac {1(2)}{2} = 1$ , $i_2 = \frac {2(3)}{2} = 3$ , $i_3 = \frac {3(4)}{2} = 6$ , $i_4 = \frac {4(5)}{2} = 10$ ....

Now, we have $\space i_{62} = \dfrac {62(63)}{2} = 1953\space$ and $\space i_{63} = \dfrac {63(64)}{2} = 2016$ . This means $\space 1954^{th}$ to $\space 2016^{th}$ , including $\space 2000^{th}$ , terms are $\space \boxed {63}$ .

just use formula for consecutive integers from binomial expansion. (n/2)(n+1) = 2000 n = 63