Definition:Automorphic Number
Jump to navigation
Jump to search
Definition
An automorphic number is a positive integer all of whose powers end in that number.
Sequence of Automorphic Numbers
The sequence of automorphic numbers begins as:
\(\ds 1\) | \(:\) | \(\ds 1^2\) | \(\ds = 1\) | |||||||||||
\(\ds 5\) | \(:\) | \(\ds 5^2\) | \(\ds = 25\) | |||||||||||
\(\ds 6\) | \(:\) | \(\ds 6^2\) | \(\ds = 36\) | |||||||||||
\(\ds 25\) | \(:\) | \(\ds 25^2\) | \(\ds = 625\) | |||||||||||
\(\ds 76\) | \(:\) | \(\ds 76^2\) | \(\ds = 3776\) | |||||||||||
\(\ds 376\) | \(:\) | \(\ds 376^2\) | \(\ds = 141 \, 376\) | |||||||||||
\(\ds 625\) | \(:\) | \(\ds 625^2\) | \(\ds = 390 \, 625\) | |||||||||||
\(\ds 9 \, 376\) | \(:\) | \(\ds 9 \, 376^2\) | \(\ds = 87 \, 909 \, 376\) |
Also known as
Some sources refer to these as curious numbers.
The term automorph for automorphic number can also sometimes be seen.
Also see
- Results about automorphic numbers can be found here.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $76$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $625$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,787,109,376$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $76$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $625$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,787,109,376$