Other than $1$, does the sequence $1,12,123,1234,\dots$ contain Fibonacci Numbers?
This is sequence A007908, and the numbers listed in this sequence is obtained by concatenating the first $n$ positive integers.
What I noticed is that some of the Fibonacci Numbers, namely $13, 34, 89,$ and $233$.
$13$ and $233$ are numbers “nearly concatenated” because $12$ and $234$ are both obtained by concatenating $n$ consecutive positive integers and the numbers adjacent to them is a Fibonacci Number.
The only Fibonacci Number that is obtained by concatenating $n$ consecutive positive integers are $34$ and $89$.
A number $n$ can be only a Fibonacci Number if $5n ^{2}\pm4$ is a perfect square.
I used Paridroid to check the values of $n\leq10^{4}$, and so far none of the numbers listed there is a Fibonacci Number.