Introduction

Back to my home page

This page is under construction, but I wanted to ensure that the results are available as soon as possible so I've put all the data in the (long) list below. Below, you will see all 637 combinations of 1 to 5 decimal digits. Each link goes to a list of all the numbers I've found that contain only those digits and also having the property that their square contains only those digits.

My search found all solutions having n digits or fewer where n is the minimum of the following:

• 15
• the smallest m such that there are at least 1000 solutions having m digits or fewer

Miscellaneous facts:

• There are 153990 total numbers in these files.
• I was inspired by Hisanori Mishima's page on tridigital squares.
• The search took about 24 hours on my MacBookPro 2.2GHz.
• These sequences have been submitted to the OEIS. You can browse them with this query.

Beware that many of the smaller sets and some of the larger sets clearly have no solutions at all, and others may have solutions, but which were too large for me to find. Others have only trivial solutions, or may be subsequences of (or identical to!) the solutions for other sets. Generally speaking, I find the solutions more interesting for larger sets.

To Do:

• Maybe get rid of the terminal zeros?
• Extend the results.
• Make the data more accessible and interesting for browsing.
• Make this page more compact, by rolling up the list into a table somehow.
• Identify the patterns (like 666...66² = a bunch of 3's, 4's, 5's and 6's ) and replace them with a single expression instead of tediously repeating all the elements.
• Extend, extend, extend...

The Data