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A376213 Prime numbers wherein a triple exchange of 3 of the digits creates two prime numbers, neither of which has a leading zero digit.

%I A376213 #19 Sep 30 2024 12:44:24
%S A376213 113,131,197,199,311,337,373,719,733,919,971,991,1013,1019,1031,1091,
%T A376213 1123,1163,1181,1193,1213,1231,1237,1279,1297,1307,1319,1321,1327,
%U A376213 1399,1439,1487,1499,1543,1549,1571,1613,1621,1637,1733,1747,1759,1777,1811,1831,1913
%N A376213 Prime numbers wherein a triple exchange of 3 of the digits creates two prime numbers, neither of which has a leading zero digit.
%C A376213 A triple exchange is a permutation of 3 elements in which all 3 three items change position. (For the triple "ABC", that would be "BCA" and "CAB".)
%e A376213 The first term is the prime 113, since 131 and 311 are also prime. Another term is 1013, since 1103 and 1301 are prime.
%o A376213 (Python)
%o A376213 from sympy import isprime
%o A376213 from itertools import combinations, permutations
%o A376213 def ok(n):
%o A376213     if n < 100 or not isprime(n): return False
%o A376213     s = list(str(n))
%o A376213     for i, j, k in combinations(range(len(s)), 3):
%o A376213         pset, w, x = {n}, s[:], s[:]
%o A376213         w[i], w[j], w[k] = w[j], w[k], w[i]
%o A376213         x[i], x[j], x[k] = x[k], x[i], x[j]
%o A376213         if w[0] != "0" and isprime(t:=int("".join(w))): pset.add(t)
%o A376213         if x[0] != "0" and isprime(t:=int("".join(x))): pset.add(t)
%o A376213         if len(pset) == 3: return True
%o A376213     return False
%o A376213 print([k for k in range(1920) if ok(k)]) # _Michael S. Branicky_, Sep 17 2024
%Y A376213 Subsequence of A225035. Cf. A375965.
%K A376213 nonn,base
%O A376213 1,1
%A A376213 _James S. DeArmon_, Sep 15 2024
%E A376213 Terms corrected by _Michael S. Branicky_, Sep 17 2024