0,1

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.

The first six terms share the digit pattern d1 d2 d3 d1 d1 d3 d1 d2 d1. Each of these terms is a (9-digit) prime corresponding to one of the 3! = 6 bijective mappings of {1,3,9} onto {d1,d2,d3}. There are no other such primes with nine or fewer digits.

Cf. A108388 (transmutable primes), A083983 (transmutable primes with two distinct digits), A108389 (transmutable primes with four distinct digits), A003459 (absolute primes), A108387 (doubly-transmutable primes).

Sequence in context: A034590 A105297 A034642 this_sequence A036744 A075130 A034611

Adjacent sequences: A109090 A109091 A109092 this_sequence A109094 A109095 A109096

base,hard,nonn

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 18 2005