A199302 - OEIS

%I #19 Sep 08 2022 08:46:00

%S 2,11,101,1021,1201,110221,111211,112111,120121,121021,122011,1000211,

%T 1010201,1020101,1022011,1022201,1101211,1102111,1102201,1111021,

%U 1112011,1120001,1120121,1120211,1121011,1201021,1201111,1210211,1212121,1221221,10002121

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

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

%o (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 */

%o (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

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

%o (Python)

%o from itertools import count, islice, product

%o from sympy import isprime

%o 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])))

%o A199302_list = list(islice(A199302_gen(),20)) # _Chai Wah Wu_, Jan 04 2022

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Nov 04 2011