Name second level of nested list in R

I have a nested list similar to the following dummy:

list1 <- list(1:3, 4:7, 8:10)
list2 <- list(2:5, 4:9, 19:23, 15:18)
list3 <- list(1:5)

nested_list <- list(list1, list2, list3)
names(nested_list) <- c("first", "second", "third")

The first level is named, while the second level is not. I would like to assign names to the second level of the list based on the first level names and pos indices, so the structure of this list would look like this:

List of 3
 $ first :List of 3
  ..$ first_1: int [1:3] 1 2 3
  ..$ first_2: int [1:4] 4 5 6 7
  ..$ first_3: int [1:3] 8 9 10
 $ second:List of 4
  ..$ second_1: int [1:4] 2 3 4 5
  ..$ second_2: int [1:6] 4 5 6 7 8 9
  ..$ second_3: int [1:5] 19 20 21 22 23
  ..$ second_4: int [1:4] 15 16 17 18
 $ third :List of 1
  ..$ third_1: int [1:5] 1 2 3 4 5

Does anyone know how to solve this? I would be grateful for help.

>Solution :

How about a for loop?

for (i in seq_along(nested_list)) {
   names(nested_list[[i]]) <- paste(names(nested_list)[i], 
                                    seq_along(nested_list[[i]]), 
                                    sep = "_")
}