Palindrome Function (#131)
To get a number’s palindrome in a programming language like python is easy. There are ways to swap between integer and string and strings can be manipulated.
>>> n = 1234 >>> int(str(n)[::-1]) 4321
But I wanted to create a mathematical function 𝑝(𝑛), which returns an integer’s palindrome. Thus 𝑝(1234) = 4321.
Firstly, I needed a way of determining the number’s size. In base 10 the length is calculated using the logarithm to said base.
Secondly, I need a way to isolate a specific digit. Using the floor function, this function returns the 𝑖-th digit (starting on the right with 𝑖 = 0).
Thirdly, both of these functions can be used to split up the number into a sum.
Fourthly, I only need to swap the power of ten at the end to get my palindrome function.
Thus the final function 𝑝(𝑛) is defined.
To check if the formula is correct, I use 1234 (as seen above).