How do I use an ifelse within a loop in R?

I have a character string ("00010000") and need to identify which position do we see the first "1". (This tells me which month a customer is active)

I have a dataset that looks like this:

id  <- c(1:5)
seq <- c("00010000","00001000","01000000","10000000","00010000")
df <- data.frame(id,seq)

I would like to create a new field identifying the first_month_active for each id.

I can do this manually with a nested ifelse function:

    df$first_month_active <-
        ifelse(substr(df$seq,1,1)=="1",1,
        ifelse(substr(df$seq,2,2)=="1",2,
        ifelse(substr(df$seq,3,3)=="1",3,       
        ifelse(substr(df$seq,4,4)=="1",4,
        ifelse(substr(df$seq,5,5)=="1",5,99 ))))) 

Which gives me the desired result:

  id  seq        first_position
  1   00010000   4
  2   00001000   5
  3   01000000   2
  4   10000000   1
  5   00010000   4

However, this is not an ideal solution for my data, which contains 36 months.

I would like to use a loop with an ifelse statement, however I am really struggling with syntax

for (i in 1:36) {
ifelse(substr(df$seq,0+i,0+i)=="1",0+i,
}

Any ideas would be greatly appreciated