bash loop in an increasing sleep time?

Question

I would like to have a while loop in bash like this:

while read i
do
    ~/bin/submit_job $i
    sleep N
done

But I would like N in sleep N to be short at the beginning, then progressively increase after the first few loops. Something like one second for the first 8, then increase in seconds like this:

 1 1 1 1 1 1 1 1 (first 8 iterations)
 2 2 2 2 2 2 2 2 
 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 
 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 
 ...

Any ideas?

Answer 1

Tested and working:

#/bin/bash
sleeptime=1
countsleeps=1
maxcount=8

while read i
do
    ~/bin/submit_job $i
    sleep $sleeptime
    let countsleeps++
    if ((countsleeps>maxcount))
    then
        countsleeps=1
        let sleeptime*=2
        if ((sleeptime>2)) ; then let maxcount*=2 ; fi
    fi
done