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The numbers in this sequence are quite low, which suggests that A083771 can be generated quite easily/quickly. It would be interesting to generate further terms to see whether their slow growth continues.
The first 5 terms of A083771 are the first 5 primes, so they all require a single primality test, hence the first 5 terms of this sequence are 1. For the 6th term in A083771 we must test 13, 17 until we finally find that 19 works, hence the 6th term of this sequence is 3.