A304390 Prime numbers p such that p squared + (p reversed) squared is also prime.

23, 41, 227, 233, 283, 401, 409, 419, 421, 461, 491, 499, 823, 827, 857, 877, 2003, 2083, 2267, 2437, 2557, 2593, 2617, 2633, 2677, 2857, 2887, 2957, 4001, 4021, 4051, 4079, 4129, 4211, 4231, 4391, 4409, 4451, 4481, 4519, 4591, 4621, 4639, 4651, 4871, 6091, 6301, 6329, 6379, 6521, 6529, 6551

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Example

The prime number 227 belongs to this sequence as 722 is 227 reversed and 227^2 + 722^2 = 572813, which is prime.

Mathematica

Select[Prime@ Range@ 850, PrimeQ[#^2 + FromDigits[ Reverse@ IntegerDigits@ #]^2] &] (* Giovanni Resta, Sep 03 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):
    r=int((str(i)[::-1]))
    t=pow(i, 2)+pow(r, 2)
    if is_prime(i):
       if is_prime(t):
          ris = ris+str(i)+", "
print(ris)
(PARI) isok(p) = isprime(p) && isprime(p^2+eval(fromdigits(Vecrev(digits(p))))^2); \\ Michel Marcus, Aug 21 2018

Crossrefs

Cf. A061783 (Luhn primes).

Subsequence of A069207. - Michel Marcus, Aug 21 2018

Sequence in context: A345099 A106969 A343816 * A309533 A331342 A306085

Adjacent sequences: A304387 A304388 A304389 * A304391 A304392 A304393

Keyword

nonn,base

Author

Pierandrea Formusa, Aug 16 2018

Status

approved