Automorphic Numbers

Automorphic Numbers

In mathematics an automorphic number (sometimes referred to as a circular number) is a number whose square "ends" in the same digits as the number itself. For example, 5² = 25, 6² = 36, 76² = 5776, and 890625² = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers. The only automorphic Kaprekar number is 1, because the square of a Kaprekar number cannot start with zero.

The sequence of automorphic numbers begins 1, 5, 6, 25, 76, 376, 625, 9376, ... (sequence A003226 in the OEIS).

For Versus While

Question: Is there any example for which the following two loops will not work same way?

/*Program 1 --> For loop*/ for (; ; ) {     }   /*Program 2 --> While loop*/ ; while () {         }

Solution:
If the body-statements contains continue, then the two programs will work in different ways

See the below examples: Program 1 will print “loop” 3 times but Program 2 will go in an infinite loop.

Example for program 1

int main() {   int i = 0;   for(i = 0; i < 3; i++)   {     printf("loop ");     continue;   }   getchar();   return 0; }

Example for program 2

int main() {   int i = 0;   while(i < 3)   {     printf("loop"); /* printed infinite times */     continue;     i++; /*This statement is never executed*/   }   getchar();   return 0; }