I will probably be accused of pedantry for this answer, but I cannot help but point out that a question like this is not a math question. There are many sequences that begin 58, 26, 16, 14, 10. There are many patterns in the sequence 58, 26, 16, 14, 10, by which I mean that there are many computer programs that compute a sequence that begins this way, and they do not all finish the sequence in the same way.

I understand that what the OP is looking for is the *simplest* pattern in the sequence, which gives the *simplest* continuation of the sequence. My objection is that "simple" here has no mathematical meaning (Kolmogorov complexity will not work because it is only defined up to a constant.)

That being said, here is my preferred answer: 58, 26, 16, 14, 10, 666, 666, 666, 666, 666,...

The pattern is that Satan put the first five numbers there to mislead clever people and the rest of them are 666.