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Primes, with at least one prime digit, that remain primes when all of their prime digits are removed.
1

%I #42 Sep 13 2022 13:04:44

%S 113,131,139,151,179,193,197,211,241,311,389,421,431,541,613,617,631,

%T 719,761,829,839,859,1013,1021,1031,1039,1051,1093,1097,1123,1153,

%U 1201,1213,1217,1229,1231,1249,1259,1279,1291,1297,1301,1321,1381,1399,1429,1439,1459,1493,1531,1549

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

%C Terms of A034844 that only have nonprime digits are not terms here. - _Michel Marcus_, Jul 19 2022

%H Michael S. Branicky, <a href="/A355856/b355856.txt">Table of n, a(n) for n = 1..10000</a>

%e The prime 179 is a term because when its prime digit 7 is removed, it remains 19, which is still a prime.

%e 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 q[n_] := (r = FromDigits[Select[IntegerDigits[n], ! PrimeQ[#] &]]) != n && PrimeQ[r]; Select[Prime[Range[250]], q] (* _Amiram Eldar_, Jul 19 2022 *)

%o (MATLAB)

%o function a = A355856( max_prime )

%o a = []; p = primes( max_prime );

%o for n = 1:length(p)

%o s = num2str(p(n));

%o s = strrep(s,'2',''); s = strrep(s,'3','');

%o s = strrep(s,'5',''); s = strrep(s,'7','');

%o m = str2double(s);

%o if m > 1

%o if isprime(m) && m ~= p(n)

%o a = [a p(n)];

%o end

%o end

%o end

%o end % _Thomas Scheuerle_, Jul 19 2022

%o (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 (Python)

%o from sympy import isprime

%o def ok(n):

%o s = str(n)

%o if n < 10 or set(s) & set("2357") == set(): return False

%o sd = s.translate({ord(c): None for c in "2357"})

%o return len(sd) and isprime(int(sd)) and isprime(n)

%o print([k for k in range(2000) if ok(k)]) # _Michael S. Branicky_, Jul 23 2022

%Y Cf. A000040, A034844, A019546.

%K nonn,base

%O 1,1

%A _Tamas Sandor Nagy_, Jul 19 2022