<think>
Okay, I need to implement the functions steps_on and hole_find as per the given interface. Let me start by understanding what each function is supposed to do.

First, the steps_on function. The description says it returns the numbers a sequence should hold, running from a first number for a stated count. So, if first is 5 and count is 3, the sequence should be [5, 6, 7]. So it's a simple arithmetic sequence starting at 'first' and incrementing by 1 for 'count' numbers. So the function can be implemented by generating a list starting from first, then first+1, up to first + count -1. That's straightforward.

Next, the hole_find function. It takes a list 'seen', and the first and count from steps_on. The goal is to find the first missing number in the sequence. If all numbers are present, return None. Otherwise, return the first missing one.

Wait, but how do I determine which numbers are missing? The 'seen' list is the sequence that's been checked. So, for example, if steps_on returns [5,6,7], then 'seen' is a list of numbers that have been checked. The hole_find function needs to check which numbers from the expected sequence are missing in 'seen' and return the first one.

But how to compute that? Let's think. The expected sequence is from first to first + count -1. So the numbers are first, first+1, ..., first + count -1. The 'seen' list is a list of numbers that have been checked. So, for each number in the expected sequence, check if it's present in 'seen'. The first one missing is the answer.

But how to efficiently check that? Well, since the expected sequence is consecutive numbers, we can iterate through each number in the expected sequence and check if it's in 'seen'. However, checking if a number is in a list is O(n) each time, which could be inefficient for large lists. But given the problem constraints, maybe it's acceptable.

Alternatively, since the expected sequence is a range, perhaps we can generate the expected numbers and compare them with the 'seen' list. But the 'seen' list could have duplicates or be in any order. Wait, but the problem says that 'seen' is the list of numbers that have been checked. So, perhaps 'seen' is a list of numbers that have been checked, but maybe not in order. However, the hole_find function is supposed to find the first missing number in the sequence.

Wait, the hole_find function is supposed to find the first missing number in the sequence generated by steps_on. So, the expected sequence is first, first+1, ..., first + count -1. The 'seen' list is the list of numbers that have been checked (maybe in some order). So, the first missing number is the first number in the expected sequence that is not present in 'seen'.

But how to check that? For example, if the expected sequence is [5,6,7], and 'seen' is [5,7], then the missing number is 6. If 'seen' is [5,6,7], then there's no missing number, so return None.

So the approach is: generate the expected sequence, then check each number in order. For each number in the expected sequence, check if it's in 'seen'. The first one not found is the answer.

But how to check if a number is in 'seen'? Since 'seen' is a list, checking with 'in' is O(n) each time. But for small counts, this is acceptable. However, if the count is large