Reverse of a number

The reverse of a number is a mathematical method to obtain from a number another written in the opposite way to the first.

For example, the reverse of 1234 is 4321.

Given a positive integer ${\displaystyle x}$, the integer which has the same digits in the reverse order is:^[1]

${\displaystyle 10^{\lfloor \log _{10}x\rfloor }x-99\sum _{k=1}^{\lfloor \log _{10}x\rfloor }{\lfloor 10^{-k}x\rfloor }10^{\lfloor \log _{10}x\rfloor -k}}$

Obtaining the reverse of a number is useful to predict if a number is Lychrel or not.^[2][3]

1. ↑ Atanes, Nicolás; Cipra, Barry (2021). "Numbers and properties". Journal of Number Theory.
2. ↑ Weisstein, Eric W. "196-Algorithm". mathworld.wolfram.com. Retrieved 2022-05-04.
3. ↑ Veselovac, Matej (2020-09-30). On Consecutive Palindromes (info:eu-repo/semantics/bachelorThesis thesis). Josip Juraj Strossmayer University of Osijek. Department of Mathematics. Chair of Pure Mathematics. Algebra and Calculus Research Group.