'How To write a function to Check for a Sequence of integers in an array in python

I'm trying to figure out why the code I wrote to find a sequence of integers in any given array is not catching all the instances. Could you help, please?

Here's the code:

def array123(nums):
  if len(nums) < 3:
    return False
  else:
    for i in range(len(nums) - 1):
      if nums[i:i + 3] == [1, 2, 3]:
        return True
      return False


Solution 1:[1]

The return False part should be indented as follows.

def array123(nums):
  if len(nums) < 3:
    return False
  else:
    for i in range(len(nums) - 1):
      if nums[i:i + 3] == [1, 2, 3]:
        return True
    return False    # This should be indented this way.

Solution 2:[2]

def array123(nums):
nums_to_string = str(nums)
if len(nums_to_string) < 3:
    return False
else:
    for i in range(len(nums_to_string) - 1):
        if nums_to_string[i:i + 3] == "123":
            return True
    return False

Solution 3:[3]

def array123(nums):
    for i in range(len(nums)-2):
        if nums[i:i + 3] == [1, 2, 3]:
            return True
    return False

 """'i' in range and then go for the length of nums because I don't know how long nums are going to be as a list. I will say -2 because I don't want to go all the way to the end. so -2 back because I'm going to be counting in steps of three."""

Sources

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Source: Stack Overflow

Solution Source
Solution 1 nilrj
Solution 2 Stef Renneboog
Solution 3