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A355856 Primes, with at least one prime digit, that remain primes when all of their prime digits are removed.

%I A355856 #42 Sep 13 2022 13:04:44
%S A355856 113,131,139,151,179,193,197,211,241,311,389,421,431,541,613,617,631,
%T A355856 719,761,829,839,859,1013,1021,1031,1039,1051,1093,1097,1123,1153,
%U A355856 1201,1213,1217,1229,1231,1249,1259,1279,1291,1297,1301,1321,1381,1399,1429,1439,1459,1493,1531,1549
%N A355856 Primes, with at least one prime digit, that remain primes when all of their prime digits are removed.
%C A355856 Terms of A034844 that only have nonprime digits are not terms here. - _Michel Marcus_, Jul 19 2022
%H A355856 Michael S. Branicky, <a href="/A355856/b355856.txt">Table of n, a(n) for n = 1..10000</a>
%e A355856 The prime 179 is a term because when its prime digit 7 is removed, it remains 19, which is still a prime.
%e A355856 The prime 136457911 is a term because when all of its prime digits, 3, 5, and 7 are removed, it remains 164911, which is still a prime.
%t A355856 q[n_] := (r = FromDigits[Select[IntegerDigits[n], ! PrimeQ[#] &]]) != n && PrimeQ[r]; Select[Prime[Range[250]], q] (* _Amiram Eldar_, Jul 19 2022 *)
%o A355856 (MATLAB)
%o A355856 function a = A355856( max_prime )
%o A355856     a = []; p = primes( max_prime );
%o A355856     for n = 1:length(p)
%o A355856         s = num2str(p(n));
%o A355856         s = strrep(s,'2',''); s = strrep(s,'3','');
%o A355856         s = strrep(s,'5',''); s = strrep(s,'7','');
%o A355856         m = str2double(s);
%o A355856         if m > 1
%o A355856             if isprime(m) && m ~= p(n)
%o A355856                 a = [a p(n)];
%o A355856             end
%o A355856         end
%o A355856     end
%o A355856 end % _Thomas Scheuerle_, Jul 19 2022
%o A355856 (PARI) isok(p) = if (isprime(p), my(d=digits(p), v=select(x->(!isprime(x)), d)); (#v != #d) && isprime(fromdigits(v));) \\ _Michel Marcus_, Jul 19 2022
%o A355856 (Python)
%o A355856 from sympy import isprime
%o A355856 def ok(n):
%o A355856     s = str(n)
%o A355856     if n < 10 or set(s) & set("2357") == set(): return False
%o A355856     sd = s.translate({ord(c): None for c in "2357"})
%o A355856     return len(sd) and isprime(int(sd)) and isprime(n)
%o A355856 print([k for k in range(2000) if ok(k)]) # _Michael S. Branicky_, Jul 23 2022
%Y A355856 Cf. A000040, A034844, A019546.
%K A355856 nonn,base
%O A355856 1,1
%A A355856 _Tamas Sandor Nagy_, Jul 19 2022