Same digits, again?
I have an integer \(n\) in my mind which satisfies following properties:
- The reciprocal \(m\) of \(n\) is a non-terminating recurring decimal
- The recurring digits of \(m\) forms a number \(p\). For example, recurring digits of reciprocal of 13 forms a number 769230 and digits of reciprocal of 9 forms 1. (Move 0 to the end if it appears at first place as I did in case of 13)
- \(p\) is the smallest number such that the digits of \(p\) are same as that of \(2p,\ 3p,\ 4p,\ 5p\) and \(6p\)
Enter your answer as \(p+n\)