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Self-inverse permutation of integers induced by the restriction of blue-code to irreducible polynomials over GF(2): a(n) = A091227(A193231(A014580(n))).
This permutation is also induced when A234747 is restricted to primes: a(n) = A000720(A234747(A000040(n))) because of the way how A234747 has been defined.
Note that each subsequence a(1)..a(A062692(j)) is closed (i.e., no cycles are leaking out) because blue code (A193231) preserves the degree of polynomials over GF(2) it operates upon.