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A226461 Numbers n such that the following are six primes: 2*n^2 +- 1, 3*n^2 +- 1, 5*n^2 +- 1.

%I A226461 #11 Feb 23 2025 01:29:20
%S A226461 6,2100,20586,669054,745590,6556122,9317496,10190796,15648732,
%T A226461 18215196,25561410,35613990,36710652,38649066,41124594,41711874,
%U A226461 46576524,48701400,49406358,59278296,70038948,74993808,75553092,83606418,84182154,88000374,92527764,98969052,100691976
%N A226461 Numbers n such that the following are six primes: 2*n^2 +- 1, 3*n^2 +- 1, 5*n^2 +- 1.
%C A226461 6 is in the sequence because the following are six primes: 71, 73, 107, 109, 179, 181.
%t A226461 spQ[n_]:=AllTrue[Flatten[{2n^2+{1,-1},3n^2+{1,-1},5n^2+{1,-1}}],PrimeQ]; Select[ Range[101*10^6],spQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 28 2015 *)
%o A226461 (Java)
%o A226461 import java.math.BigInteger;
%o A226461 public class A226461 {
%o A226461     public static void main (String[] args) {
%o A226461       for (long n = 1; n < (1L << 30); n++) {
%o A226461           long x = n*n*5;
%o A226461           BigInteger b = BigInteger.valueOf(x+1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           b = BigInteger.valueOf(x-1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           x = n*n*2;
%o A226461           b = BigInteger.valueOf(x+1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           b = BigInteger.valueOf(x-1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           x = n*n*3;
%o A226461           b = BigInteger.valueOf(x+1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           b = BigInteger.valueOf(x-1);
%o A226461           if (!b.isProbablePrime(80)) continue;
%o A226461           System.out.printf("%d, ", n);
%o A226461       }
%o A226461     }
%o A226461 }
%Y A226461 Cf. A173165.
%K A226461 nonn
%O A226461 1,1
%A A226461 _Alex Ratushnyak_, Jun 08 2013