happy 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, and the function

$$f(m)=\sum _{i=1}^{k}d_i{}^2,$$

if computing $f(n)$ and iterating that function on the result eventually leads to a fixed point of 1, then $n$ is said to be a happy number in base $b$.

For $b=2$ and $b=4$, all numbers are happy numbers. All standard positional bases have happy numbers.

Title	happy number
Canonical name	HappyNumber
Date of creation	2013-03-22 16:19:56
Last modified on	2013-03-22 16:19:56
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A63