Starting 2020 with a post on a 4 simple digit number, which happens to be a palindrome - 1221
On the face of it it just like any other palindrome number - Divisible by 11 like any palindrome for e.g
Let's dig a little deeper and unearth some of the unique characteristics that's otherwise not so obvious
1. 1221 is product of 407 and 3 and 407 in turn is the largest 3 digit Armstrong number. Not only that 407 is sum of 343 and 64 - 343 is a palindrome while 64 is a perfect square or a cube. 407 is a multiple of 37 and 11 and we would see more of it later
2. 12 multiplied by 21 gives 252 which is a palindrome again
3. Now let's insert number 3 right in the middle of 12 and 21 which results in the five digit palindrome 12321 - No surprises there as only the middle digit has been introduced. Let's look further though
4. 12321 is a perfect square itself - 111 * 111. 111 like 407 earlier is a multiple of 37!
5. Let's add 123 + 21 (first 3 digits and last 2 digits) and the resulting number is 144 which is a perfect square and 144 written in reverse (441) is a perfect square. More importantly 144 is 12 * 12 (which are the first two digits of 1221) while 441 is 21 * 21 (which are the last two digits of 1221)!
6. Now add 12 + 321 (first 2 digits and last 3 digits) and the resulting number is 333 which is a multiple of 37 again!
7. Now let's look at a subset of 1221 which is 121 - again a perfect square and a palindrome as well!
1221 or 12321 or 121 form a unique pattern and as I mentioned earlier, we need to dig deeper and analyze to unearth some of these invisible patterns
Would be back with more in my subsequent posts!
On the face of it it just like any other palindrome number - Divisible by 11 like any palindrome for e.g
Let's dig a little deeper and unearth some of the unique characteristics that's otherwise not so obvious
1. 1221 is product of 407 and 3 and 407 in turn is the largest 3 digit Armstrong number. Not only that 407 is sum of 343 and 64 - 343 is a palindrome while 64 is a perfect square or a cube. 407 is a multiple of 37 and 11 and we would see more of it later
2. 12 multiplied by 21 gives 252 which is a palindrome again
3. Now let's insert number 3 right in the middle of 12 and 21 which results in the five digit palindrome 12321 - No surprises there as only the middle digit has been introduced. Let's look further though
4. 12321 is a perfect square itself - 111 * 111. 111 like 407 earlier is a multiple of 37!
5. Let's add 123 + 21 (first 3 digits and last 2 digits) and the resulting number is 144 which is a perfect square and 144 written in reverse (441) is a perfect square. More importantly 144 is 12 * 12 (which are the first two digits of 1221) while 441 is 21 * 21 (which are the last two digits of 1221)!
6. Now add 12 + 321 (first 2 digits and last 3 digits) and the resulting number is 333 which is a multiple of 37 again!
7. Now let's look at a subset of 1221 which is 121 - again a perfect square and a palindrome as well!
1221 or 12321 or 121 form a unique pattern and as I mentioned earlier, we need to dig deeper and analyze to unearth some of these invisible patterns
Would be back with more in my subsequent posts!
