A199303 Palindromic primes in the sense of A007500 with digits '0', '1' and '3' only.
3, 11, 13, 31, 101, 113, 131, 311, 313, 1031, 1033, 1103, 1301, 3011, 3301, 10301, 10333, 11003, 11311, 13331, 30011, 30103, 31013, 31033, 33013, 33301, 101333, 110311, 113011, 113131, 131311, 133033, 133103, 301331, 301333, 330331, 333101, 333103, 1000033, 1001003, 1001303, 1003001
Offset: 1
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..6114
Programs
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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
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Mathematica
Flatten[{#,IntegerReverse[#]}&/@Select[FromDigits/@Tuples[{0,1,3},7],AllTrue[ {#,IntegerReverse[ #]},PrimeQ]&]]//Union (* Harvey P. Dale, Sep 12 2023 *) -
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 */ -
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 -
Python
from itertools import product from sympy import isprime 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