<p>Since your data is sequential and there is dependency between numbers, it should be possible to train a recurrent neural network. The recurrent weights take care of the relationship between numbers.  </p>

<p>As a general rule of thumb, the more uncorrelated input sequences you have, the better it is. This survey article can help you get started with RNN: <a href="https://arxiv.org/abs/1801.01078" rel="nofollow noreferrer">https://arxiv.org/abs/1801.01078</a></p>
Predicting patterns in number sequences
<p>My problem is as follows. As inputs I have sequences of whole numbers, around 200-500 per sequence. Each number in a sequence is marked as good or bad. The first number in each sequence is always good, but whether or not subsequent numbers are still considered good is determined by which numbers came before it. There's a mathematical function which governs how the numbers affect those that come after it but the specifics of this function are unknown. All we know for sure is it starts off accepting every number and then gradually starts rejecting numbers until finally every number is considered bad. Out of every sequence only around 50 numbers will ever be accepted before this happens.</p>

<p>It is possible that the validity of a number is not only determined by which numbers came before it, but also by whether these numbers were themselves considered good or bad.</p>

<p>For example: (<strong>good</strong> numbers in bold)</p>

<ul>
<li><p><strong>4 17 8 47 52</strong> 18 <strong>13</strong> <strong>88</strong> 92 55 8 <strong>66</strong> 76 85 36 ...</p></li>
<li><p><strong>92 13 28</strong> 12 <strong>36 73 82</strong> 14 18 <strong>10</strong> 11 <strong>21</strong> 33 98 1 ...</p></li>
</ul>

<p>Attempting to determine the logic behind the system through guesswork seems like an impossible task. So my question is, can a neural network be trained to predict if a number will be good or bad? If so, approximately how many sequences would be required to train it? (assuming sequences of 200-500 numbers that are 32 bit integers)</p>