Pattern recognition is a very hard part of Math and Logic. Unfortunately pattern recognition hepls us to find recursive or explicite formulas for a given series. Sometimes it only inspires us to find the way, which leads us to the formula.
I believe, that there is no recursive or explicite formula for this series:
What is the next number ?
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First you can recognize, that these numbers are all primes.
Then you can recognize, that these primes only use primes as digits ( 2 ; 3 ; 5 ; 7 )
Thus the next number is 3 5 3
See here