A199302 Palindromic primes in the sense of A007500 with digits '0', '1' and '2' only.

2, 11, 101, 1021, 1201, 110221, 111211, 112111, 120121, 121021, 122011, 1000211, 1010201, 1020101, 1022011, 1022201, 1101211, 1102111, 1102201, 1111021, 1112011, 1120001, 1120121, 1120211, 1121011, 1201021, 1201111, 1210211, 1212121, 1221221, 10002121

Offset: 1

Author

M. F. Hasler, Nov 04 2011

Keywords

• nonn
• base

Comments

All terms except for the initial 2 start and end in the digit 1.

Crossrefs

Cf. A020449 - A020472, A199325 - A199329, A199303 - A199306.

Programs

Magma

[p: p in PrimesUpTo(10^8) | Set(Intseq(p)) subset [0..2] and IsPrime(Seqint(Reverse(Intseq(p))))];  // Bruno Berselli, Nov 07 2011

PARI

allow=Vec("012");forprime(p=1,default(primelimit),setminus( Set( Vec(Str( p ))),allow)&next;isprime(A004086(p))&print1(p",")) /* better use the much more efficient code below */

PARI

a(n=50,list=0,L=[0,1,2],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 count, islice, product
from sympy import isprime
def A199302_gen(): return (n for n in (int(t+''.join(s)) for l in count(0) for t in '12' for s in product('012',repeat=l)) if isprime(n) and isprime(int(str(n)[::-1])))
A199302_list = list(islice(A199302_gen(),20)) # Chai Wah Wu, Jan 04 2022