user
9 months ago
[deleted]
Automorphic Numbers
1 pointsposted 9 months ago
by syllablehq3 Comments
syllablehq
9 months 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
9 months 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