Let a(0) = 1. Either, a(n) = the smallest prime not yet occurring in the sequence that, when written in binary, it is a substring in the binary representation of a(n-1); or, if no such prime exists, a(n) = the smallest prime not yet occurring that when written in binary, a(n-1) is contained as a substring within it.

A175310

Let a(0) = 1. Either, a(n) = the smallest prime not yet occurring in the sequence that, when written in binary, it is a substring in the binary representation of a(n-1); or, if no such prime exists, a(n) = the smallest prime not yet occurring that when written in binary, a(n-1) is contained as a substring within it.