I have defined sequence numbers as integers that produce a known or recognizable sequence of numbers when you take their inverse and calculate its digital expansion.
I call them sequence numbers because I have not found another name for them (except “Mr. B,s Super-Duper Fantastic Arithmetically Accurate and Magically Mathematical Sequence Numbers” – a catchy title but much too long).
An example can be found at http://www.futilitycloset.com/2012/01/08/math-notes-76/ . I call these type 1 sequence numbers. I have found other numbers that for one reason or another do not fit my definition of sequence numbers but produce “sequence number-ish” results. I call these type 2 sequence numbers, and I will publish these from time to time along with type 1 sequence numbers.
I will also try to publish short explanations about how I found some of these numbers and about the properties of some of these numbers.