0,1

This sequence is a subsequence of A108386 and of A108388. See the latter for the definition of transmutable primes and many more comments. Are any terms here doubly-transmutable also; i.e., terms of A108387? Palindromic too? Terms also of some other sequences cross-referenced below? a(7)=771319973999 is also a reversible prime (emirp). a(12)=9311933973733 also has the property that simultaneously removing all its 1's (93933973733), all its 3s (9119977) and all its 9s (3113373733) result in primes (but removing all 7s gives 93119339333=43*47*59*83*97^2, so a(12) is not also a term of A057876). Any additional terms have 14 or more digits.

a(0)=133999337137 is the smallest transmutable prime with four distinct digits (1,3,7,9):

exchanging all 1's and 3's: 133999337137 ==> 311999117317 (prime),

exchanging all 1's and 7's: 133999337137 ==> 733999331731 (prime),

exchanging all 1's and 9's: 133999337137 ==> 933111337937 (prime),

exchanging all 3's and 7's: 133999337137 ==> 177999773173 (prime),

exchanging all 3's and 9's: 133999337137 ==> 199333997197 (prime) and

exchanging all 7's and 9's: 133999337137 ==> 133777339139 (prime).

No smaller prime with four distinct digits transmutes into six other primes.

Cf. A108386 (Primes p such that p's set of distinct digits is {1, 3, 7, 9}), A108388 (transmutable primes), A083983 (transmutable primes with two distinct digits), A108387 (doubly-transmutable primes), A006567 (reversible primes), A002385 (palindromic primes), A068652 (every cyclic permutation is prime), A107845 (transposable-digit primes), A003459 (absolute primes), A057876 (droppable-digit primes).

Sequence in context: A072718 A034652 A015402 this_sequence A017542 A104832 A105295

Adjacent sequences: A108386 A108387 A108388 this_sequence A108390 A108391 A108392

base,hard,nonn

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 02 2005