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# happy number

$n=\sum_{{i=1}}^{k}d_{i}b^{{i-1}}$ |

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.

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## Mathematics Subject Classification

11A63*no label found*

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