# 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 HappyNumber 2013-03-22 16:19:56 2013-03-22 16:19:56 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11A63