# There are all these kinds of names for numbers?

You remember the other day I got a hotel room number 407 and I had written about how it is an Armstrong number? (which is a special case of Narcissistic numbers). Well that got me thinking what are the other kind of numbers that are out there? I was surprised to find out there are so many different names.

Let’s start with **Narcissistic numbers** itself. Do you know when is a number narcissistic?

If the number is equal to the sum of each one of its digits raised to the number of digits, then it is narcissistic. Let’s take the example of 407. There are 3 digits in it and 407 = 4 cubed plus 0 cubed plus 7 cubed. That makes it a narcissistic number. Or take 1634. There are 4 digits in it. 1634 = 1 to the power 4 PLUS 6 to the power 4 PLUS 3 to the power 4 PLUS 4 to the power 4.

Apparently there are only 88 such narcissistic numbers.

Do you know what a **perfect number** is?

If all the divisors of a number (other than the number itself) add up to the number itself, it is called perfect. For example, 28. The factors are 1, 2, 4, 7 and 14. And they add to 28. Similary, 6 is a perfect number as is 496 and 8128.

Did you know there are **happy numbers and sad numbers**?

Take a number like 19. The digits are 1 and 9. Square them up and add. You get 1+81 = 82. Do the same again – 8 squared plus 2 squared is 68. Do again – you get 100. And then you are stuck on a loop of 1.

Now try 7. You get 49. Then 97. Then 130. Then 10. Then 1

There are a few numbers where if you keep doing this – square the digits and add and then keep doing – they will get stuck in a loop (either at 1 or a loop that does not have 1). Such numbers are called happy numbers. Every other number is a sad number!

What is a **strong numbe**r?

If you add the factorials of the digits of the number and you land back at the original number, it is called strong number! Try 145. 1 factorial PLUS 4 factorial PLUS 5 factorial is 1 + 24 + 120 = 145. Thus it is a strong number

You know what is a **circular number**?

If the square of the number ends with the number itself, it is a circular number. e.g. 6, 25 …

Now Google and find out what is a **vampire number**? or an **odious number**? **hoax number**? **pandigital number**?

If you find more interesting numbers, do write back…

Sanjoy BanerjeeonThanks for the great share of number it is really interesting.

Kaushik DattaonHow about Ramanujan number?

Rajib RoyonI think I remember that – sum of two cubes in two different ways right?

Kaushik DattaonRajib Roy yes 1729=12^3+1^3=10^3+9^3 this was a taxi cab number as far as I remember

Kaushik DattaonIn recent times, I got interested in 2 numbers twin prime and prime gap

Rajib RoyonI knew about twin primes but I had to google prime gap…

Kaushik DattaonRajib Roy yes. Twin prime is an instance of prime gap.

Bill LuskonCool stuff. I Remember a method to confirm a product of a long multiplication was to “Cast out 9’s.”

Rajib RoyonIndeed! Later computer algorithms used the same concept to make sure data transfers were happening reliably (checksum digit method)

Ambarish MitraonOne interesting number is 142857. If you multiply it with 2, 3, 4, 5, 6 – then the result is all a circular representation of the digits in 142857.

285714

428571

571428

714285

857142

See that all multiples of 2, 3, 4, 5, 6 are circle of the digits in the number 142857.

X 7=999999

Rajib RoyonAren’t they called PERSISTENT number or something?

Ambarish MitraonDon’t know the term.

Madhusudhan M. Reddyon26 is the only number sandwiched between a square and a cube. Or, is it?

Rajib RoyonMadhusudhan, well 0 is sandwiched between -1 and 1 (they being -1 cubed and 1 squared)

Madhusudhan M. ReddyonSorry, my statement sounded a bit relaxed when I said sandwiched between a square and a cube. However, it strictly means, x**2 + 1 = z = y**3 – 1, and z = 26 and only 26?

Kaushik Dattaon(a+b)/a=a/b Golden ratio. Just saw it again.