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A199303 Palindromic primes in the sense of A007500 with digits '0', '1' and '3' only.

%I A199303 #25 Sep 12 2023 14:50:25
%S A199303 3,11,13,31,101,113,131,311,313,1031,1033,1103,1301,3011,3301,10301,
%T A199303 10333,11003,11311,13331,30011,30103,31013,31033,33013,33301,101333,
%U A199303 110311,113011,113131,131311,133033,133103,301331,301333,330331,333101,333103,1000033,1001003,1001303,1003001
%N A199303 Palindromic primes in the sense of A007500 with digits '0', '1' and '3' only.
%H A199303 Chai Wah Wu, <a href="/A199303/b199303.txt">Table of n, a(n) for n = 1..6114</a>
%t A199303 Flatten[{#,IntegerReverse[#]}&/@Select[FromDigits/@Tuples[{0,1,3},7],AllTrue[ {#,IntegerReverse[ #]},PrimeQ]&]]//Union (* _Harvey P. Dale_, Sep 12 2023 *)
%o A199303 (PARI) allow=Vec("013"); forprime(p=1, default(primelimit), setminus( Set( Vec( Str( p ))), allow)&next; isprime(A004086(p))&print1(p", ")) /* for illustrative purpose only: better use the code below */
%o A199303 (PARI) a(n=50,list=0,L=[0,1,3],needpal=1)={ for(d=1,1e9, u=vector(d,i,10^(d-i))~; forvec(v=vector(d,i,[1+(i==1&!L[1]),#L]), isprime(t=vector(d,i,L[v[i]])*u) || next; needpal & !isprime(A004086(t)) & next; list & print1(t","); n-- || return(t)))}  \\ _M. F. Hasler_, Nov 06 2011
%o A199303 (Magma) [p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0, 1, 3] and IsPrime(Seqint(Reverse(Intseq(p))))]; // _Bruno Berselli_, Nov 07 2011
%o A199303 (Python)
%o A199303 from itertools import product
%o A199303 from sympy import isprime
%o A199303 A199303_list = [n for n in (int(''.join(s)) for s in product('013',repeat=12)) if isprime(n) and isprime(int(str(n)[::-1]))] # _Chai Wah Wu_, Dec 17 2015
%Y A199303 Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.
%K A199303 nonn,base
%O A199303 1,1
%A A199303 _M. F. Hasler_, Nov 04 2011