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{align}

25641 \times \color{blue}{1} \times 4 &= \color{blue}{1}02564 \\

25641 \times \color{blue}{2} \times 4 &= \color{blue}{2}05128 \\

25641 \times \color{blue}{3} \times 4 &= \color{blue}{3}07692 \\

25641 \times \color{blue}{4} \times 4 &= \color{blue}{4}10256 \\

25641 \times \color{blue}{5} \times 4 &= \color{blue}{5}12820 \\

25641 \times \color{blue}{6} \times 4 &= \color{blue}{6}15384 \\

25641 \times \color{blue}{7} \times 4 &= \color{blue}{7}17948 \\

25641 \times \color{blue}{8} \times 4 &= \color{blue}{8}20512 \\

25641 \times \color{blue}{9} \times 4 &= \color{blue}{9}23076

\end{align}

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!