I would like to find a square whose digits are $n^2$ and $(n+1)^2$ lined up in this order.
$49$ is the only example I know, which has $2^2=4$ and $(2+1)^2=9$ lined up.
So basically, I would like to find a square in the sequence $14, 49, 916, 1625, 2536, \cdots$.
Google told me that there is no such number until $n=10^5$, so I suspect there is no such number except $49$, but I don't know how to prove it.
Also, my language ability is limited, so please tell me if there is a better way to phrase this question.