Extracting nth character till the end of string in R

I'm trying to extract the nth character onwards in a string, using R. Here's my data:

StringField
example_string1
example_string2
example_string3
example_string4
example_string5
example_string6
example_string7
example_string8
example_string9
example_string10
example_string11
example_string12

I want to extract only the numbers after example_string, so the result would be:

1
2
3
4
5
6
7
8
9 
10
11
12

I've tried something along the lines of:

df$unique_number <- substr(df$stringField, 15:)

to indicate I want everything from the 15th position onward, till the end of the string. Any thoughts on an easy way to accomplish what I'm trying to do? thanks!