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

113, 131, 139, 151, 179, 193, 197, 211, 241, 311, 389, 421, 431, 541, 613, 617, 631, 719, 761, 829, 839, 859, 1013, 1021, 1031, 1039, 1051, 1093, 1097, 1123, 1153, 1201, 1213, 1217, 1229, 1231, 1249, 1259, 1279, 1291, 1297, 1301, 1321, 1381, 1399, 1429, 1439, 1459, 1493, 1531, 1549

Offset

1,1

Comments

Terms of A034844 that only have nonprime digits are not terms here. - Michel Marcus, Jul 19 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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

Prog

(MATLAB)
function a = A355856( max_prime )
    a = []; p = primes( max_prime );
    for n = 1:length(p)
        s = num2str(p(n));
        s = strrep(s, '2', ''); s = strrep(s, '3', '');
        s = strrep(s, '5', ''); s = strrep(s, '7', '');
        m = str2double(s);
        if m > 1
            if isprime(m) && m ~= p(n)
                a = [a p(n)];
            end
        end
    end
end % Thomas Scheuerle, Jul 19 2022
(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
(Python)
from sympy import isprime
def ok(n):
    s = str(n)
    if n < 10 or set(s) & set("2357") == set(): return False
    sd = s.translate({ord(c): None for c in "2357"})
    return len(sd) and isprime(int(sd)) and isprime(n)
print([k for k in range(2000) if ok(k)]) # Michael S. Branicky, Jul 23 2022

Crossrefs

Cf. A000040, A034844, A019546.

Sequence in context: A214847 A069488 A131648 * A180441 A378415 A180407

Adjacent sequences: A355853 A355854 A355855 * A355857 A355858 A355859

Keyword

nonn,base

Author

Tamas Sandor Nagy, Jul 19 2022

Status

approved