[math-fun] Digital silliness

[Edwin Clark]

On Tue, 10 Jan 2006, David Wilson wrote:

> For a number n, let f(n) be the set of numbers gotten by splitting n^2 at the 0 
> digits.  For example
> 
> 29648^2 = 879003904
> 
> so f(29648) = { 4, 39, 879 }
> 
> Let S be the smallest set of numbers containing 2 and fixed by f.  What is the 
> largest element of S?

I assume you mean by S: The smallest set of positive integers satisfying 

1. 2 is in S
2. if n is in S then f(n) is a subset of S

In this case, my (not very extensive) experiments lead me to conjecture 
that every positive integer which contains no 0 is in S. 

--Edwin