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Python 3, 136 127 126 bytes

r=range
f=lambda n:sorted(int(''.join(str(i)for i in r(1+k,j+k)if l+k-i))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

# f=lambda n:sorted( int(''.join(str(i) for i in r(1+k,j+k)  if l+k-i)) for k in r(n) for j in r(4,n) for l in r(2,j-1))[:n]
#            ──┬──                      ─────────┬────────    ───┬───   ──────┬──────  ──────┬──────  ────────┬──────── ─┬─
#              │                                 │               │            │              │                │          └── selection of the n first numbers
#              │                                 │               │            │              │                └── loop to remove missing element
#              │                                 │               │            │              └── loop for the dimension of the list n to be sure we miss nothing xD
#              │                                 │               │            └── loop on the n in op description 
#              │                                 │               └── Test to remove missing element
#              │                                 └── loop on {n, n+1 ...} in the op description
#              └──── sort the list

Python 3, 136 127 126 122 bytes

r=range
f=lambda n:sorted(int(''.join(str(i+k)for i in r(1,j)if l-i))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

# f=lambda n:sorted( int(''.join(str(i+k) for i in r(1,j)   if l-i)) for k in r(n) for j in r(4,n) for l in r(2,j-1))[:n]
#            ──┬──                        ───────┬───────    ───┬──  ──────┬──────  ──────┬──────  ────────┬──────── ─┬─
#              │                                 │              │          │              │                │          └── selection of the n first numbers
#              │                                 │              │          │              │                └── loop to remove missing element
#              │                                 │              │          │              └── loop for the dimension of the list n to be sure we miss nothing xD
#              │                                 │              │          └── loop on the n in op description 
#              │                                 │              └── Test to remove missing element
#              │                                 └── loop on {n, n+1 ...} in the op description
#              └──── sort the list

Thanks to @mbomb007 and @FricativeMelon for their help

r=range
f=lambda n:sorted(int(''.join(str(i)for i in r(1+k,j+k)if l+k-i))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

r=range
f=lambda n:sorted(int(''.join(str(i)for i in r(1+k,j+k)if l+k-i))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

Python 3, 136 127 bytes

r=range
f=lambda n:sorted(int(''.join(str(i)for i in r(1+k,j+k)if i!=l+k))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

Python 3, 136 127 126 bytes

r=range
f=lambda n:sorted(int(''.join(str(i)for i in r(1+k,j+k)if l+k-i))for k in r(n)for j in r(4,n)for l in r(2,j-1))[:n]

Explanation

# f=lambda n:sorted( int(''.join(str(i) for i in r(1+k,j+k)  if l+k-i)) for k in r(n) for j in r(4,n) for l in r(2,j-1))[:n]
#            ──┬──                      ─────────┬────────    ───┬───   ──────┬──────  ──────┬──────  ────────┬──────── ─┬─
#              │                                 │               │            │              │                │          └── selection of the n first numbers
#              │                                 │               │            │              │                └── loop to remove missing element
#              │                                 │               │            │              └── loop for the dimension of the list n to be sure we miss nothing xD
#              │                                 │               │            └── loop on the n in op description 
#              │                                 │               └── Test to remove missing element
#              │                                 └── loop on {n, n+1 ...} in the op description
#              └──── sort the list