Sed script that removes specific lines in `seq` output

I have a file to process with sed but I am not quite familiar with the commands with capital letters used for multi-line patterns. I use seq to test the script and I have converted it to the problem described below. The sed script and expected output are also attached. I believe the script can be written in a much better way but I am not sure how to do it.

Problem description:

Filter the output of seq $m, where $m is a given integer. removing the $n^{rm th}$ line if either $n-2$, $n-1$, $n$, or $n+1$ contains the digit $7$.

Sed script (together with the seq pipe, note this is GNU sed):

seq "$m"|sed ':c N;N;N;:a N;s/.*n.*7.*n.*n.*n//g;tc;P;s/^[^n]*n//g;ba;'

I believe setting two labels (a and c) is not necessary.

Edit: There seems to be a nicer alternative, based on the answer to Delete 5 Lines Before and 6 Liens After Pattern Match Using sed, as follows,

seq "$m"|sed 'N;/7/!{P;D};:b N;s/n/&/3;Tb;d'

This avoids writing out a lot of N; and n‘s explicitly. Still I believe it can be improved.

Sample output for m=100

1
2
3
4
5
10
11
12
13
14
15
20
21
22
23
24
25
30
31
32
33
34
35
40
41
42
43
44
45
50
51
52
53
54
55
60
61
62
63
64
65
82
83
84
85
90
91
92
93
94
95
100

Related: Extension of Game of Sevens Challenge at CodeGolf

N;/7/!{P;D}

Nice job there, this very concisely (and clearly) allows you to capture both lines $n$ and $n+1$.

:b N;s/n/&/3;Tb;d

Now the loop that follows it is mostly redundant. You are essentially appending lines of input until you are left with $4$ lines in total. You already have $2$ in your pattern space and need $2$ more, i.e. lines $n-1$ and $n-2$, which can simply be expressed in N;N followed by a d.