A Staggering Sequence

Let the following sequence:
- $c_1=2$
- $c_n=\frac{c_{n-1}\times (c_{n-1}+n+140)}{n}$

- What is the first index $n$ such as $c_n$ is not an integer?
- How many digits does the integer part of $c_n$ have?

Answer format: n,number of digits

[My timing : < 1 sec]