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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A304390.

Sequence in context: A108406 A051268 A159911 * A133959 A133960 A031931

Adjacent sequences: A319138 A319139 A319140 * A319142 A319143 A319144

Keyword

nonn,base,look

Author

Pierandrea Formusa, Sep 11 2018

Status

approved