A304390 - OEIS

%I #22 Sep 03 2018 11:54:04

%S 23,41,227,233,283,401,409,419,421,461,491,499,823,827,857,877,2003,

%T 2083,2267,2437,2557,2593,2617,2633,2677,2857,2887,2957,4001,4021,

%U 4051,4079,4129,4211,4231,4391,4409,4451,4481,4519,4591,4621,4639,4651,4871,6091,6301,6329,6379,6521,6529,6551

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

%H Seiichi Manyama, <a href="/A304390/b304390.txt">Table of n, a(n) for n = 1..5000</a>

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

%t Select[Prime@ Range@ 850, PrimeQ[#^2 + FromDigits[ Reverse@ IntegerDigits@ #]^2] &] (* _Giovanni Resta_, Sep 03 2018 *)

%o (Python)

%o nmax=10000

%o def is_prime(num):

%o     if num == 0 or num == 1: return(0)

%o     for k in range(2, num):

%o        if (num % k) == 0:

%o            return(0)

%o     return(1)

%o ris = ""

%o for i in range(nmax):

%o     r=int((str(i)[::-1]))

%o     t=pow(i,2)+pow(r,2)

%o     if is_prime(i):

%o        if is_prime(t):

%o           ris = ris+str(i)+","

%o print(ris)

%o (PARI) isok(p) = isprime(p) && isprime(p^2+eval(fromdigits(Vecrev(digits(p))))^2); \\ _Michel Marcus_, Aug 21 2018

%Y Cf. A061783 (Luhn primes).

%Y Subsequence of A069207. - _Michel Marcus_, Aug 21 2018

%K nonn,base

%O 1,1

%A _Pierandrea Formusa_, Aug 16 2018