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A108389 Transmutable primes with four distinct digits. 3
133999337137, 139779933779, 173139331177, 173399913979, 177793993177, 179993739971, 391331737931, 771319973999, 917377131371, 933971311913, 997331911711, 1191777377177, 9311933973733, 9979333919939 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..13.


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 * A172561 A172600 A172704

Adjacent sequences:  A108386 A108387 A108388 * A108390 A108391 A108392




Rick L. Shepherd, Jun 02 2005



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