Number Names
I was looking into the number 2022, trying to find something cool about it. (Honestly, I think it’s a little cumbersome to say and does not have the most visual appeal). During my research to redeem it, I discovered that 2022 is classified as a “Hardash Number:“ a number divisible by the sum of its digit. 2022/(2+0+2+2) = 337. Now that’s a little cool. I’ll let you decide for yourself if this is enough to vindicate 2022, but it got me thinking about all of the hidden numbers. Who knew that there was such a thing as Hardash Numbers? And the thought that some person probably dedicated years of his life to studying and finding all of these numbers is a little funny to me. And also the thought that there are so many numbers we use every day that have this hidden component to them. This began my quest for other classified numbers. Everyone knows about primes and Fibonacci numbers, but imagine all of the other ones that could be out there.
To aid in my search, I discovered this online database for sequences and numbers: OEIS
Basically, this is the Dewey decimal system for math. First I discovered Mersenne primes. A Mersenne number is found with the equation [2^n - 1]. What is cool, is that all of these terms are represented with just 1’s in binary form. The primes from this sequence are 3, 7, 31, 127, 8191, 131071. There are actually rewards for those who can find Mersenne primes of 1 million, 10 million, 100 million digits. Mersenne primes are also connected to perfect numbers, discovered by Euclid and then furthered by Euler. A perfect number is a number equal to the sum of its divisors. For example, 6 = 1+2+3. Perfect numbers are considered “even“ if they are Mersenne primes. 2^n − 1 is prime then 2^(n−1)(2^n − 1) is a perfect number. This connection between Mersenne numbers and perfect numbers aids in computer programing along with general number theory.
The next number term I found was hemachandra numbers. Now, these are actually the Fibonacci sequence, but what I found most interesting was the difference in relation to the natural world. While the Fibonacci sequence is most commonly found in sunflower seed spiral, leave positions, and other organic materials, hamachandra numbers were developed from musical and rhythmic sources. In a type of poetry, Sanskrit, each symbol can either be long or short. The number of distinct “rhythms,“ or long/short beat combinations, corresponds with the hemachandra series, or Fibonacci sequence following the pattern 1, 2, 3, 5, 8, 13 […]. For example, a rhythm with 5 beats can have 8 distinct rhythms. This is a really cool example of how two different mathematicians in two different parts of the world discovered the same sequence that connects two different parts of the natural world.
The next fun definition that I found belonged to ordinal numbers. Now, you probably use ordinal numbers every day: numbers that denote the position of something. For example, 1st, 2nd, 3rd, all ordinal numbers. Expanding that definition, Wikipedia claims that “A set S is an ordinal if and only if S is strictly well-ordered with respect to set membership and every element of S is also a subset of S.” Basically, the number 6 can be represented by the set {0, 1, 2, 3, 4, 5}, and following the definition, 3 (represented by {0, 1, 2}) satisfies this rule. Honestly, I don’t fully understand ordinals beyond this definition, but they do form this really cool spiral (shown below) that I hope one day to understand.
There are so many other classifications for number, and series of numbers that a random guy found and defined hundreds of years ago. Maybe one day, you too will be able to put your own name on a random set of numbers.