Friday, September 25, 2015

Summary - Where are we?


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  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. 


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