Re: [math-fun] Digital silliness

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