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

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..6114

Mathematica

Flatten[{#, IntegerReverse[#]}&/@Select[FromDigits/@Tuples[{0, 1, 3}, 7], AllTrue[ {#, IntegerReverse[ #]}, PrimeQ]&]]//Union (* Harvey P. Dale, Sep 12 2023 *)

Prog

(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
(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
(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

Crossrefs

Cf. A020449 - A020472, A199325 - A199329, A199302 - A199306.

Sequence in context: A111488 A125308 A260044 * A244047 A020451 A018450

Adjacent sequences: A199300 A199301 A199302 * A199304 A199305 A199306

Keyword

nonn,base

Author

M. F. Hasler, Nov 04 2011

Status

approved