The Aperiodical 

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The magic number 25641

By Christian Lawson-Perfect. Posted October 27, 2016

Reader of the site Bhaskar Hari Phadke has written in to tell us this fun fact about the number $25641$. It’s easier to show than to describe, so here goes:

$$\begin{array}{rl}25641\times 1\times 4& =102564\\ 25641\times 2\times 4& =205128\\ 25641\times 3\times 4& =307692\\ 25641\times 4\times 4& =410256\\ 25641\times 5\times 4& =512820\\ 25641\times 6\times 4& =615384\\ 25641\times 7\times 4& =717948\\ 25641\times 8\times 4& =820512\\ 25641\times 9\times 4& =923076\end{array}$$

A good one to challenge a young person with.

I did a little bit of Sloanewhacking and found a couple of sequences containing $25641$ which almost, but don’t quite, describe this property. So, semi-spoiler warning: you might enjoy A256005 and A218857. I’d like to come up with the ‘magic number’ which looks the least like it’ll have this property – any ideas?

Thanks, Bhaskar!