Let us call a positive integer $n$ 'fortunate' if the sum of its digits is a multiple of 7, and 'superfortunate' if it is fortunate and if none of the numbers $n+1, n+2,\dots, n+12$ is fortunate. Find the smallest superfortunate number.
I tried finding a superfortunate number so I could create an upper bound and work back, but I couldn't find any superfortunate numbers. If anyone could help, it would be greatly appreciated!!
Thanks!!
Best Answer
$993$ is the smallest superfortunate number.
You can obtain this by letting the digits of $n$ be $$... a 9 9 ... 9 b$$ where $a<9$ and there are, say, $k$ 9s. Then look at the results of adding 1,2,3 ... ,12.