The names you describe can be described by a regular expression, hence the set of all names is a regular language. relating to this little adventure please! I'd love to hear any comments/trivia etc. What is the right way to describe the problem outlined in the first few paragraphs, what do I need to learn to figure it out? I'm presuming that my adventure isn't anything extraordinary at all and maths is full of this unexpected relationships stuff, true? Maths is full of this sort of thing isn't it? And I'm just looking at one little problem from one very specific angle, this is just the tip of the iceberg here isn't it?
With a quick Google search I found some of these sequences in all sorts of strange places, some examples include transformations of Lucas Numbers, solutions to Kakuro / Addoku / Soduku puzzles, repunits, the coordinates of geodesic faces, even the Ishango bone, which I'd never heard of before. I looked at all sorts of things, I wish I'd documented it more, I was just idly mucking around with a spreadsheet and Googling sequences. Going from there, looking at all sorts of different things, amongst them the sequences of numbers in different placeholder columns in the tables, differences between numbers in different columns and/or tables etc. The first table appears in OEIS as A002452. I haven't got around to looking into these yet, because I got fascinated by the first table. I also generated a table for digits appearing no more than twice or thrice: 0-999 991 I stopped there because beyond that's where it started taking to long to calculate and I didn't want to get sidetracked optimizing. I started with the constraint that a digit could only appear once, so in the range 0-99 there are 9 invalid sequences, 11, 22, 33 etc., leaving 91 valid 'names of God'. Not being very knowledgable about math, I thought I'd write a program iterate over ranges and count all the elements that match the above condition, then put the results in a spreadsheet to see if a clear pattern of some kind emerged that would let me write an algorithm to determine the number of valid sequences in a given range. I started with digits repeating in base 10 numbers, at heart it's the same problem as letters repeating in an alphabet. Out of curiosity, I started playing around with determining how many valid sequences there are in a range. In Arthur C Clarke's story "The 9 Billion Names of God" the names of God are all possible sequences in an unspecified alphabet, having no more than nine characters, where no letter occurs more than three times in succession. I've done the first dozen or so Euler problems and intend to continue with that when I have time. My maths isn't great (I can't read notation) but I'm a competent programmer and reasonable problem solver. TLDR I go on a math adventure and get overwhelmed :)
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