A319141 Prime numbers p such that p squared + p reversed is also prime.

211, 223, 271, 283, 433, 463, 691, 823, 859, 2017, 2029, 2251, 2269, 2293, 2341, 2347, 2593, 2647, 2833, 2851, 2857, 2887, 4153, 4327, 4507, 4513, 4903, 6091, 6361, 6421, 6481, 6529, 6871, 6949, 8011, 8059, 8161, 8209, 8287, 8419, 8467, 8707, 8803, 8929, 8971

Offset: 1

Author

Pierandrea Formusa, Sep 11 2018

Keywords

• nonn
• base
• look

Comments

All terms == 1 (mod 6). - Robert Israel, Sep 13 2018

Examples

			271 belongs to this sequence as 271 squared is 73441 and 271 reversed is 172 and the sum of 73441 and 172 is 73613, which is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A304390.

Programs

Maple

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L));
end proc:
filter:= t -> isprime(t) and isprime(t^2+revdigs(t)):
select(filter, [seq(t,t=1..10^4,6)]); # Robert Israel, Sep 13 2018

Mathematica

Select[Prime@Range@1120, PrimeQ[#^2 + FromDigits[Reverse@IntegerDigits@#]] &] (* Vincenzo Librandi, Sep 14 2018 *)

PARI

forprime(p=1, 9000, if(ispseudoprime(p^2 + eval(concat(Vecrev(Str(p))))), print1(p, ", "))) \\ Felix Fröhlich, Sep 12 2018

Python

nmax=10000
def is_prime(num):
    if num == 0 or num == 1: return(0)
    for k in range(2, num):
       if (num % k) == 0:
           return(0)
    return(1)
ris = ""
for i in range(nmax):
    if is_prime(i):
       r=int((str(i)[::-1]))
       t=pow(i,2)+r
       if is_prime(t):
          ris = ris+str(i)+","
print(ris)