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For example a pattern could be 1,3,5 and you could say the next number is 7 because you add 2 each time. But what if you are given just the number 1 or 1,3? You can't say that the pattern is you add 2 each time confidently right? Another example are raven's progressive matrices, https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices where you are to identify the next element in the pattern, and it seems like most commonly are 3x3 grids, but how are these determined? For any arbitrary pattern, is there a needed number of steps to determine the next element in the list (and thus the pattern)?

user289602
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  • So you're assuming that, first of all, it's possible to uniquely determine all the numbers of a sequence every time. But this cannot be true: I could just come up with some numbers from the top of my head: $$ 594, 54238, 4213295, 1, 49823 $$ How would you know what the next is? I literally randomly selected some numbers. – Matti P. Dec 09 '19 at 06:59
  • Well there's no pattern to this, so the question does not apply. Right? Or for example you couldn't determine a pattern giving integers provided by a pseudo-random number generator but I would imagine there is a pattern given a hashing algorithm (given enough time and resources I'd imagine) – user289602 Dec 09 '19 at 07:04
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    There is OEIS, online encyclopedia of integer sequences, and if you type your numbers into it it will give you named sequences where they occur in that order. If you try 1,3,5 it will give you multiple pages of hits, and in most of them the next number is not 7. There is no reconstructing a "pattern" from finitely many numbers, there are always infinitely many "patterns" that have them as the initial segment. – Conifold Dec 09 '19 at 07:50

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