“Die Sin For”: 102564. Dyson Numbers
A Dyson number, also called n-parasitic number (in base 10) is a positive natural number which can be multiplied by n by moving the rightmost digit of its decimal representation to the front.
Criterion: The numbers do not start with zero and hence fit the actual definition.
If X = 421052631578947368, it is a dyson number, since:
2X = 842105263157894736 which is a right rotation of X by 1 step.
The number X is also called a double-trouble number in the number system with base 10. Any number system with base p >= 2, however, has many such double-trouble numbers.
So, just like when n=2, for an n-parasitic number, where doubling the number is same as right shifting the number, for all n in 1≤n≤9, we can find dyson numbers. Infact, there are many such n-parasitic Dyson numbers.
Here is my solution to the smallest positive Dyson numbers from 0–9 in the base 10 number system.