Do numbers like \(12=3\times 4\) and \(56=7×8\) have a name? Are there any more?

@unknown Notice that the first has digits 1,2,3,4 in order. The second has digits 5,6,7,8 in order.

@j Thank you for telling me! Numbers that are consecutive in order on the formula are beautiful. I search example of additon etc on OEIS too!

I did not find it at all, but a few memorandum of information that I could know for now. 

@vam103 You're looking for integer solutions to \(f(a) = 0\) where \(f(a) = a\cdot10^{\lceil \log_{10} (a+1)\rceil} + (a+1) - (a+2)(a+3)\). That odd operating with the ceil \(\lceil\cdot\rceil\) and \(\log\) is concatentation.

\(a=1,\) and \(a=5\) are two. \(f\) is easier to differentiate than it looks at first glance, just remember that floor and ceiling functions are locally constant. Use that to see that \(f\) is increasing before \(a=1,\) and decreasing after \(a=5\). They're the only two.

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