# Palindrome Function

2016-07-02, post № 131

**mathematics**, **programming**, **Python**, #p(n), #sum

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).