

A108389


Transmutable primes with four distinct digits.


3



133999337137, 139779933779, 173139331177, 173399913979, 177793993177, 179993739971, 391331737931, 771319973999, 917377131371, 933971311913, 997331911711, 1191777377177, 9311933973733, 9979333919939
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OFFSET

0,1


COMMENTS

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 doublytransmutable also; i.e., terms of A108387? Palindromic too? Terms also of some other sequences crossreferenced 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.


LINKS

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


EXAMPLE

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.


CROSSREFS

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 (doublytransmutable primes), A006567 (reversible primes), A002385 (palindromic primes), A068652 (every cyclic permutation is prime), A107845 (transposabledigit primes), A003459 (absolute primes), A057876 (droppabledigit primes).
Sequence in context: A072718 A034652 A015402 * A172561 A172600 A172704
Adjacent sequences: A108386 A108387 A108388 * A108390 A108391 A108392


KEYWORD

base,hard,nonn


AUTHOR

Rick L. Shepherd, Jun 02 2005


STATUS

approved



