How to identify the pattern of a sequence 
Are there some particular methods for identifying the following types of number series?



*

*$6, 10, 19, 44, 93, \cdots$ (Difference being prime no's square starting from 2)

*$1, -2, 15, 52, -512, \cdots $ ( $^*2-4,\ ^*-6+3,\ ^*4-8,\ ^*-10+5$, and so on)

*$4, -2, -7, 25, 95,\cdots$ ( $^*-1+2,\ ^*2-3,\ ^*-3+4,\ ^*4-5$, and so on)

I mean they do not follow the arithmetic or geometric series nor do their common difference seem to follow any AM-GM pattern. So, is there any generalized mathematical theorems on these types of number series? Or we have to do it on a trial & error basis using intuition?


I think it is possible with neural networks, specifically with recurrent neural network.
From the nodes of the neural network, you may be able to come up with a complex notation using forward propagation.
However, there are still quite a lot of hyperparameters that you need to define first. For example:
1) Regularization 
2) number of hidden layers
3) length of the input (for RNN) and so on....
Some of these hyperparameters like the number of hidden layers will end up in the final forward propagation.
