Palindromic number

Palindromic number in C#

In other words it has reflectional symmetry across a vertical axis.

The term palindromic is derived from palindrome, which refers to a word (such as rotor , tenet) whose spelling is unchanged when it's letters are reversed.

Consider a number \(n > 0\) in base \(b \ge 2\) where it is written in standard notation with \() k + 1\) digits \(a_{i}\) as:

$$n = \sum _{i=0}^{k}a_{i}b^{i}$$

where:

\(0 \le a_{i} < b\) for all \(i\) and \(a_{k} \ne 0\)

Then \(n\) is palimendric if and only if \(a_{i} = a_{k -i}\) for all \(i\). Zero is written \(0\) in any base and is also palindromic by definition.

Note:

• Although palindromic number are most often considered in the decimal system, the concept of _**palindromicity**_ can be applied to the natural numbers in any numeral system.

Example of 20 first palindromic numbers (in decimal)

$$0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, \cdots$$

The folowing code in \(C\), will check if the given number by user is pelindromic number or not.

/*
This code help us to look if a given number is palindromic or not.
*/

#include <stdio.h>

int palindromic_no(int number, int reverse, int reaminder);

int main(){

    //Enter a number to check.
    int num;
    printf("Enter number: ");
    scanf("%d", &num);

    int rev=0;
    int rem;

    //check is done here
    palindromic_no(num, rev, rem);
    return 0;
}

int palindromic_no(int number, int reverse, int remainder){

    //reversing the given number
    int origin_no = number;
    while (number != 0)
    {
        remainder=number%10;
        reverse = reverse*10 +remainder;
        number /= 10;
    }

    //check if given number is pelindromic number or not.
    if (origin_no == reverse){
        printf("Number: %d, is palindromic number", origin_no);
    }else{
        printf("Number: %d, is not palindromic number", origin_no);
    }
    return 0;
    }