• We perform a loop over all files starting with "p-" in the current directory.
• The first instruction in the loop ensures that the file exists and is a workaround for empty directories (the reason why this is necessary is that on this forum, you will always be told not to parse the output of ls, so something like FILES=$(ls p-*); for FILE in $FILES; do ... would be considered a no-go).
• Then, we extract the numerals between p- and _n needed to generate the first level of your directory structure using awk (as you suspected, with regular expressions), the same for the numerals between n- and _a for the second level.
• Third, we check if the directories for the first and second level of your intended directory structure already exist. If not, we create them.
• Last, we move the file to the target directory.

• We perform a loop over all files starting with "p-" in the current directory.
• The first instruction in the loop ensures that the file exists and is a workaround for empty directories (the reason why this is necessary is that on this forum, you will always be told not to parse the output of ls, so something like FILES=$(ls p-*); for FILE in $FILES; do ... would be considered a no-go).
• Then, we extract the numerals between p- and _n needed to generate the first level of your directory structure using awk (as you suspected, with regular expressions), the same for the numerals between n- and _a for the second level. The idea is to use the match function which not only looks for the place where the specified regular expression occurs in your input, but also gives you the "completed" value of all elements enclosed in round brackets ( ... ) in the array "fields".
• Third, we check if the directories for the first and second level of your intended directory structure already exist. If not, we create them.
• Last, we move the file to the target directory.

• For one, since the directory names are actually p-<number> and n-<number>, the same as in your filename, we could have let awk do the work to extract these characters for us, too, by writing match($1,"(^p-[[:digit:]]+)_(n-[[:digit:]]+)_[[:print:]]*",fields)

• We can further offload work to awk by having it generate the directory-subdirectory path at the same time with a suitable argument of print:

awk '{match($1,"(^p-[[:digit:]]+)_(n-[[:digit:]]+)_[[:print:]]*",fields); print fields[1] "/" fields[2]}'

would readily yield (e.g.) p-12345/n-384 for file p-12345_n-384_a-583.pdf. If we combine that with the usage of mkdir -p as indicated by @wurtel, the script could look like

for FILE in p-*
do
    if [[ ! -f $FILE ]]; then continue; fi

    TARGET="$(awk '{match($1,"(^p-[[:digit:]]+)_(n-[[:digit:]]+)_[[:print:]]*",fields); print fields[1] "/" fields[2]}' <<< $FILE)"
    echo "move $FILE to $TARGET"

    mkdir -p "$TARGET"
    mv $FILE $TARGET
done

As already noted, the short answer is "yes".

The long answer is: You can do it with a bash script that uses awk to extract the filename elements you want to base your directory structure on. It could look something like this (where more emphasis is placed on readability than "one-liner" compactness).

#!/bin/bash


for FILE in p-*
do
    if [[ ! -f $FILE ]]; then continue; fi

    LVL1="$(awk '{match($1,"^p-([[:digit:]]+)_[[:print:]]*",fields); print fields[1]}' <<< $FILE)"
    LVL2="$(awk '{match($1,"^p-([[:digit:]]+)_n-([[:digit:]]+)_[[:print:]]*",fields); print fields[2]}' <<< $FILE)"

    echo "move $FILE to p-$LVL1/n-$LVL2"
    if [[ ! -d "p-$LVL1" ]]
    then
    mkdir "p-$LVL1"
    fi

    if [[ ! -d "p-$LVL1/n-$LVL2" ]]
    then
    mkdir "p-$LVL1/n-$LVL2"
    fi

    mv $FILE "p-$LVL1/n-$LVL2"
done

To explain:

• We perform a loop over all files starting with "p-" in the current directory.
• The first instruction in the loop ensures that the file exists and is a workaround for empty directories (the reason why this is necessary is that on this forum, you will always be told not to parse the output of ls, so something like FILES=$(ls p-*); for FILE in $FILES; do ... would be considered a no-go).
• Then, we extract the numerals between p- and _n needed to generate the first level of your directory structure using awk, the same for the numerals between n- and _a for the second level.
• Third, we check if the directories for the first and second level of your intended directory structure already exist. If not, we create them.
• Last, we move the file to the target directory.

For more information, have a look at the Advanced bash scripting guide and the GNU Awk Users Guide.

As already noted, the short answer is "yes".

The long answer is: You can do it with a bash script that uses awk to extract the filename elements you want to base your directory structure on. It could look something like this (where more emphasis is placed on readability than "one-liner" compactness).

#!/bin/bash


for FILE in p-*
do
    if [[ ! -f $FILE ]]; then continue; fi

    LVL1="$(awk '{match($1,"^p-([[:digit:]]+)_[[:print:]]*",fields); print fields[1]}' <<< $FILE)"
    LVL2="$(awk '{match($1,"^p-([[:digit:]]+)_n-([[:digit:]]+)_[[:print:]]*",fields); print fields[2]}' <<< $FILE)"

    echo "move $FILE to p-$LVL1/n-$LVL2"
    if [[ ! -d "p-$LVL1" ]]
    then
    mkdir "p-$LVL1"
    fi

    if [[ ! -d "p-$LVL1/n-$LVL2" ]]
    then
    mkdir "p-$LVL1/n-$LVL2"
    fi

    mv $FILE "p-$LVL1/n-$LVL2"
done

To explain:

• We perform a loop over all files starting with "p-" in the current directory.
• The first instruction in the loop ensures that the file exists and is a workaround for empty directories (the reason why this is necessary is that on this forum, you will always be told not to parse the output of ls, so something like FILES=$(ls p-*); for FILE in $FILES; do ... would be considered a no-go).
• Then, we extract the numerals between p- and _n needed to generate the first level of your directory structure using awk (as you suspected, with regular expressions), the same for the numerals between n- and _a for the second level.
• Third, we check if the directories for the first and second level of your intended directory structure already exist. If not, we create them.
• Last, we move the file to the target directory.

For more information, have a look at the Advanced bash scripting guide and the GNU Awk Users Guide.

Once you are more firm in scripting and regular expressions, you can make this much more compact; in the above script, for example, the generation of the directory/subdirectory path could easily be contracted to just one awk call.