trimorphic number

Given a base $b$ integer

$$n=\sum _{i=1}^k{d}_i{b}^{i-1}$$

where $d_1$ is the least significant digit and $d_k$ is the most significant, if it’s also the case that the $k$ least significant digits of $n^3$ are the same of those of $n$, then $n$ is called a trimorphic number.

All automorphic numbers (with $m=1$) are also trimorphic numbers, but not all trimorphic numbers are 1-automorphic.

Title	trimorphic number
Canonical name	TrimorphicNumber
Date of creation	2013-03-22 16:21:32
Last modified on	2013-03-22 16:21:32
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	5
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A63