An interesting trick of number 421. What is so special about the number 421?
Number 421 is the smallest prime number formed by the powers of two in logical order from right to left.
Follow the given steps and you will notice an interesting loop of 4...2...1...
1) Select any whole number.
2) If it is an even number,divide by 2; If it is an odd number, multiply by 3 and add 1 to it.
3) Keep on repeating the process mentioned in step 2. We'll see that after a while the value 4,2,1 repeats itself.
Example: Lets pick a number, say, 23.
23 is an odd number; so multiply by 3 and add 1 to it;
(23 × 3) + 1 = 70
70 is an even number; so divide by 2;
70 / 2 = 35
35 is an odd number; so multiply by 3 and add 1 to it;
(35 × 3) + 1 = 106
106 is an even number; so divide by 2;
106 / 2 = 53
53 is an odd number; so multiply by 3 and add 1 to it;
(53 × 3) + 1 = 160
160 is an even number; so 160 / 2 = 80
80 is an even number; so 80 / 2 = 40
40 is an even number; so 40 / 2 = 20
20 is an even number; so 20 / 2 = 10
10 is an even number; so 10 / 2 = 5
5 is an odd number; so (5 × 3) + 1 = 16
16 is an even number; so 16 / 2 = 8
8 is an even number; so 8 / 2 = 4
4 is an even number; so 4 / 2 = 2
2 is an even number; so 2 / 2 = 1
1 is an odd number; so (1 × 3) + 1 = 4
4 is an even number; so 4 / 2 = 2
2 is an even number; so 2 / 2 = 1
. . . . . . . . . . . . . . . . .
We see that the loop 4..2..1 goes on and on.
