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%I #11 Dec 15 2023 09:00:28
%S 133999337137,139779933779,173139331177,173399913979,177793993177,
%T 179993739971,391331737931,771319973999,917377131371,933971311913,
%U 997331911711,1191777377177,9311933973733,9979333919939,19979113377173,31997131171111,37137197179931,37337319113911
%N Transmutable primes with four distinct digits.
%C 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.
%H Michael S. Branicky, <a href="/A108389/b108389.txt">Table of n, a(n) for n = 1..1000</a>
%e a(0)=133999337137 is the smallest transmutable prime with four distinct digits (1,3,7,9):
%e exchanging all 1's and 3's: 133999337137 ==> 311999117317 (prime),
%e exchanging all 1's and 7's: 133999337137 ==> 733999331731 (prime),
%e exchanging all 1's and 9's: 133999337137 ==> 933111337937 (prime),
%e exchanging all 3's and 7's: 133999337137 ==> 177999773173 (prime),
%e exchanging all 3's and 9's: 133999337137 ==> 199333997197 (prime) and
%e exchanging all 7's and 9's: 133999337137 ==> 133777339139 (prime).
%e No smaller prime with four distinct digits transmutes into six other primes.
%Y 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).
%K nonn,base
%O 1,1
%A _Rick L. Shepherd_, Jun 02 2005
%E a(14) and beyond from _Michael S. Branicky_, Dec 15 2023
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