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##Jelly, 8 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
De¢

Try it online!

Explanation:

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
D     Convert input to list ( '123' -> [1, 2, 3])
e¢    This checks to see if the decimal list is in the list of our previous link.

Jelly, 8 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
De¢

Try it online!

Explanation:

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
D     Convert input to list ( '123' -> [1, 2, 3])
e¢    This checks to see if the decimal list is in the list of our previous link.

##Jelly, 8 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
De¢

Explanation

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
D     Convert input to list ( '123' -> [1, 2, 3])
e¢    This checks to see if the decimal list is in the list of our previous link.

##Jelly, 8 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
De¢

Try it online!

Explanation:

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
D     Convert input to list ( '123' -> [1, 2, 3])
e¢    This checks to see if the decimal list is in the list of our previous link.

##Jelly, 7 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
e¢

Explanation

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
e¢    This checks to see if the input (implicit input to the dyad `e`)
      is in the list of our previous link.

##Jelly, 8 bytes

Not as short as Dennis's answer (duh), but I'm quite proud of myself for getting the results I wanted out of Jelly.

9Rṡ3
De¢

Explanation

9R    Push 1-9 to the stack
ṡ3    Slice up the stack in parts of 3, overlapping
      This gives us [1,2,3], [2,3,4], ..., [7,8,9]
D     Convert input to list ( '123' -> [1, 2, 3])
e¢    This checks to see if the decimal list is in the list of our previous link.