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!

I must be missing something, all I see is that the leading digit of the product is the same as the digit being multiplied.

Disregard that, I see it now

That property applies to any 5 figure number where the first 2 figures are 25

For some integer n, any number between $10^{n}/40$ and $10^{n}/36$ will have this property, so it’s all a matter of which one of those you think will look the least special. One that is interesting is 27601:

$27601 \times 7 \times 4=772828$ for example, which is nice because $4 \times 7=28$. Similarly, $27601 \times 3 \times 4=331212$.