#!/bin/bash

HOSTNAME=128.128.0.6
SLEEP_TIME=10m
BACKOFF_LIMIT=128 #seconds

while true; do
    ts=1
    while [ $ts -le $BACKOFF_LIMIT ]; do
        /bin/ping -c 1 $HOSTNAME > /dev/null
        if [ $? -eq 0 ]; then
            break
        elif [ $ts -eq $BACKOFF_LIMIT ]; then
            /sbin/reboot
        fi
        sleep $ts
        ts=$(( ts * 2 ))
    done
    sleep $SLEEP_TIME
done