Multiply 142857 by 3, you get 428571, the same digits, but with a
circular shift : the 1st digit has become the last.
We can rotate in the reverse direction : 142857 × 5 = 714285, the last digit has become the first.
Such a number (142857) is a "Derviche number", rotating by multiplication.
Even more, when multiplying by 2,3,4,5,6, we get all its circular shifts.
Excluding such excess, just find the smallest number, which multiplied by 2 rotates one digit right
Rotate one digit left ?
Same questions when multiplying by 3, 4, ... 9