sed N と P 複数行のコマンドオプションが期待どおりに動作しません。

データサンプル：

output=$(cat <<EOF
This is line 1.
This is line 2.
This is line 3.
This is line 4.
This is line 5.
This is line 6.
EOF
)
echo "${output}" > ~/data8.txt

次の2行が同じ結果を返すのはなぜですか？

sed '{
N
3,$P
}' ~/data8.txt

This is line 1. 
This is line 2. 
This is line 3. 
This is line 3. 
This is line 4. 
This is line 5. 
This is line 5. 
This is line 6.


sed '{
N
4,$P
}' ~/data8.txt

上記の行が返されると予想します。

This is line 1.
This is line 2.
This is line 3.
This is line 4.
This is line 4.
This is line 5.
This is line 5.
This is line 6.

しかし、次のように返されます。

This is line 1.
This is line 2.
This is line 3.
This is line 3.
This is line 4.
This is line 5.
This is line 5.
This is line 6.

この奇妙な動作を解決するのに役立ちますか？