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By my definition of (a nontrivial) transmutable prime, each digit of each term must be capable of being an ending digit of a prime, so this sequence is a subsequence of A108387, primes p such that p's set of distinct digits is {1,3,7,9}. The repunit primes (A004022), which would otherwise trivially be (doubly-)transmutable and primes whose distinct digits are other proper subsets of {1,3,7,9} are excluded here by the two-disjoint-pair condition.

a(n) is a term iff a(n) is prime and binomial(m,2) 'transmutations' (see example) of a(n) are different primes. A083983 is the subsequence for m=2: one transmutation (The author of A083983, Amarnath Murthy, calls the result of such a digit-exchange a self-complement. {Because I didn't know until afterwards that this sequence was a generalization of A083983 and as this generalization always leaves some digits unchanged for m>2, I've chosen different terminology.}). A108389 ({1,3,7,9}) is the subsequence for m=4: six transmutations. Each a(n) corresponding to m=3 (depending upon its set of distinct digits) and having three transmutations is also a member of A108382 ({1,3,7}), A108383 ({1,3,9}), A108384 ({1,7,9}), or A108385 ({3,7,9}). The condition m>=2 only eliminates the repunit (A004022) and single-digit primes. The condition m<=4 is not a restriction because if there were more distinct digits, they would include even digits or the digit 5, in either case transmuting into a composite number. Some terms such as 1933 are reversible primes ("Emirps": A006567) and the reverse is also transmutable. The transmutable prime 3391933 has three distinct digits and is also a palindromic prime (A002385). The smallest transmutable prime having four distinct digits is A108389(0) = 133999337137 (12 digits).

See the definitions of "transmutable" and "transmutation" in A108388. Some primes with two distinct digits, namely all terms of A083983, can be considered trivially fully-transmutable. This subsequence of A108388 considers only transmutable primes with more distinct digits. These are primes such that all permutations of assignments of their distinct digits to their shared digit pattern produces primes. (Contrast this with the absolute primes, A003459, where all permutations of the digits themselves produce primes.). Fully-transmutable primes with three distinct digits occur in sets of 3! = 6. Fully-transmutable primes with four distinct digits, if any, would occur in sets of 4! = 24 and would also be a subsequence of A108389.