user
13 hours ago
[deleted]
Automorphic Numbers
1 pointsposted 13 hours ago
by syllablehq3 Comments
syllablehq
13 hours ago
It just occurred to me that it was weird how 6^n always ends in 6. And that it never occured to me before that that was weird. 5s of course do that too. And I wondered what numbers do it in other bases and why. And I found this nice blog post talking about it. And was surprised to find that very large numbers also have this property.
syllablehq
13 hours ago
Thinking about this more... and just thinking out loud here. So this pattern essentially happens when: In whatever base you're in a number x^n gives an end of "0" plus a remainder of the number x. So a number would be automorphic if ((x^n - 1) * n) always ends in "0" (to whatever length that matches the number).
E.g. ((6^n - 1) * 6) or ((376^n - 1) * 376) Cool