QST: Related to working of `as_index` in pandas groupby 
- [X] I have searched the [[pandas] tag](https://stackoverflow.com/questions/tagged/pandas) on StackOverflow for similar questions.

- [x] I have asked my usage related question on [StackOverflow](https://stackoverflow.com).

---

#### Question about pandas

```
import pandas as pd
import numpy as np
df = pd.DataFrame(np.random.randint(0,10,size=(10, 4)), columns=list('ABCD'))
df.A = df.agg('City_{0[A]}'.format, axis=1)
df.index = (df.index)*int(np.random.randint(6,23)**0.5)+int(np.random.randint(2,23))
```

**This is my df:**


 A | B | C | D 
-- | -- | -- | -- 
City_2 | 3 | 7 | 3
City_0 | 4 | 8 | 9
City_1 | 1 | 2 | 1
City_5 | 5 | 0 | 9
City_5 | 1 | 6 | 0
City_0 | 3 | 8 | 6
City_7 | 2 | 6 | 6
City_1 | 6 | 0 | 2
City_8 | 6 | 2 | 4
City_2 | 2 | 5 | 6

If I do 

`df.groupby([df.index//5,df.A], as_index=True).mean()`
or 
`df.groupby([df.index//5,df.A]).mean()`

**Result:**

|   |        | B | C | D |
|--:|-------:|--:|--:|--:|
|   |    A   |   |   |   |
| 1 | City_2 | 3 | 7 | 3 |
| 2 | City_0 | 4 | 8 | 9 |
| 3 | City_1 | 1 | 2 | 1 |
|   | City_5 | 5 | 0 | 9 |
| 4 | City_0 | 3 | 8 | 6 |
|   | City_5 | 1 | 6 | 0 |
| 5 | City_7 | 2 | 6 | 6 |
| 6 | City_1 | 6 | 0 | 2 |
|   | City_8 | 6 | 2 | 4 |
| 7 | City_2 | 2 | 5 | 6 |


So If do `.reset_index()`

I will get this (that index with no column name will get name as `level_0` ): 

  level_0 | A | B | C | D
-- | -- | -- | -- | -- 
1 | City_2 | 3 | 7 | 3
2 | City_0 | 4 | 8 | 9
3 | City_1 | 1 | 2 | 1
3 | City_5 | 5 | 0 | 9
4 | City_0 | 3 | 8 | 6
4 | City_5 | 1 | 6 | 0
5 | City_7 | 2 | 6 | 6
6 | City_1 | 6 | 0 | 2
6 | City_8 | 6 | 2 | 4
7 | City_2 | 2 | 5 | 6

The same is not with the `as_index=False`
 `df.groupby([df.index//5,df.A], as_index=False).mean()` will give me


 A | B | C | D 
-- | -- | -- | -- 
City_2 | 3 | 7 | 3
City_0 | 4 | 8 | 9
City_1 | 1 | 2 | 1
City_5 | 5 | 0 | 9
City_0 | 3 | 8 | 6
City_5 | 1 | 6 | 0
City_7 | 2 | 6 | 6
City_1 | 6 | 0 | 2
City_8 | 6 | 2 | 4
City_2 | 2 | 5 | 6


I will lose the `groupby index info`.  

**My question:**
shouldn't be  `as_index=False` give `df.index//5` column also. Or `as_index` is designed to work like this only. 

