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A159292 Pandigital emirps.

%I A159292 #29 Apr 28 2024 11:31:10
%S A159292 10124389567,10124563789,10124597683,10124635897,10124673859,
%T A159292 10124687359,10124695783,10124735689,10124795683,10124867359,
%U A159292 10124958673,10124965387,10124965783,10125364897,10125693847,10125749863,10125784639,10125938467,10126387549,10126457893,10126498573
%N A159292 Pandigital emirps.
%C A159292 There are 413842 11-digit terms. - _Jud McCranie_, Jul 03 2013 [in light of the comment below, this was independently computed and confirmed to be correct by _Michael S. Branicky_, Apr 06 2024]
%C A159292 The above statement [by _Jud McCranie_] is uncertain, as the contributed b-file was wrong (missing terms) from a(436) on. At this point, one has to consider permutations of 10223456789, before coming back, for n > 495, to permutations of 10123456789 starting with 10231.... - _M. F. Hasler_, Apr 06 2024
%H A159292 Michael S. Branicky, <a href="/A159292/b159292.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..435 from Jud McCranie, terms 436..500 corrected and added by M. F. Hasler)
%F A159292 Intersection of A006567 and A050288. - _M. F. Hasler_, Apr 05 2024
%o A159292 (PARI) L=List(); append(N=10123456789, M=Vecsmall([2,3,3]))=forperm(digits(N),p, cmp(p[3..5],M)>0 && break; isprime(P=fromdigits(Vec(p)))&& isprime(fromdigits(Vecrev(p)))&& listput(L, P))
%o A159292 append(); append(10223456789); #A159292=Set(L) \\ _M. F. Hasler_, Apr 05 2024
%o A159292 (Python)
%o A159292 from sympy import isprime
%o A159292 from itertools import count, islice, product
%o A159292 def emirp(s):
%o A159292     r = s[::-1]
%o A159292     return r != s and isprime(int(s)) and isprime(int(r))
%o A159292 def agen(): # generator of terms
%o A159292     for d in count(11):
%o A159292         for f in "1379":
%o A159292             for m in product("0123456789", repeat=d-2):
%o A159292                 for e in "1379":
%o A159292                     t = f + "".join(m) + e
%o A159292                     if len(set(t)) == 10 and emirp(t):
%o A159292                         yield int(t)
%o A159292 print(list(islice(agen(), 100))) # _Michael S. Branicky_, Apr 09 2024
%Y A159292 Cf. A006567 (emirps), A050288 (pandigital primes).
%K A159292 nonn,base
%O A159292 1,1
%A A159292 _Lekraj Beedassy_, Apr 08 2009
%E A159292 Erroneous terms corrected and more terms from _M. F. Hasler_, Apr 05 2024