OK, let, see where we are at.
I have shown you how to create Sequence Numbers that generate counting sequences that count as high as you want them to.
I have shown you how to create Sequence Numbers that generate multiplication sequences for many (but not all) positive integers.
I have shown you how to create Sequence Numbers that generate a list of the powers of a number for any positive integer.
I have shown you how to create Sequence Numbers that generate combinatorial functions in the form of C (n, m) for any number m that you desire. (The sequences shows the number of ways to select m items from a group of n items.)
And I have shown you how to create Sequence Numbers for many varieties of Fibonacci like sequences that start with a zero (or a series of zeros) and a one.
I have also shown you a way to find Sequence Numbers that generate other number sequences that do not fit into one of the categories above – if a Sequence Number is Possible.
As far as I know this is the current state of the art for finding and working with what I have called Sequence Numbers. (Well, first I wanted to call them “Mr. B’s Super-duper-fantastic Arithmetically Accurate and Mathematically Mystical Sequence Number. It’s catchy, but a little long.)
I have not found other people working on these kinds of numbers on the web. And I have found very few mentions of these kinds of numbers (other than the Sequence Number 998,001, which generates a digital sequence that counts from 000 to 997).
I was simply a guy who saw a number that had a very interesting property, and wondered how many other numbers had a similar property. I started looking for them and found a few.
I think other people could find more. I doubt that I have found them all. If you do find an interesting Sequence Number, and want to share it with me, please contact me at firstname.lastname@example.org. Please also tell me if I have permission to post it on this website, with your name attached.
I will continue to work on this, and will publish my findings on this website to share with you.
I will also tell you about other numbers or fractions that do not fit the definition of a sequence number, but produce interesting “sequence number-ish” results.
I will also let you know if a find an easy way to do more lengthy calculations, using even larger sequence numbers than I have used in the past. Wolfram Alpha has been a great help so far, but even Wolfram Alpha limits the size of Sequence Numbers that I can use, and the length of the output of my calculations. I will also share with you interesting items that I find in the Online Encyclopedia of Integer Sequences (OEIS), which has also been a great help to me in my work.
An I will occasionally share with you some of my failures so that you might find a solution for.
I am still recovering from a stroke, so I may not post every day. If you don’t see new posts for a few days please forgive me, and keep checking back to see what is new in the world of Sequence Numbers.
P.S. I also run another math blog where I share a wider selection of interesting mathematical items that you may find interesting and a bit less mathematically challenging than this site. MathematicalMysteryTour.blogspot.com