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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. 1

%I

%S 6,2100,20586,669054,745590,6556122,9317496,10190796,15648732,

%T 18215196,25561410,35613990,36710652,38649066,41124594,41711874,

%U 46576524,48701400,49406358,59278296,70038948,74993808,75553092,83606418,84182154,88000374,92527764,98969052,100691976

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

%C 6 is in the sequence because the following are six primes: 71, 73, 107, 109, 179, 181.

%t 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 (Java)

%o import java.math.BigInteger;

%o public class A226461 {

%o public static void main (String[] args) {

%o for (long n = 1; n < (1L << 30); n++)

%o long x = n*n*5;

%o BigInteger b = BigInteger.valueOf(x+1);

%o if (!b.isProbablePrime(80)) continue;

%o b = BigInteger.valueOf(x-1);

%o if (!b.isProbablePrime(80)) continue;

%o x = n*n*2;

%o b = BigInteger.valueOf(x+1);

%o if (!b.isProbablePrime(80)) continue;

%o b = BigInteger.valueOf(x-1);

%o if (!b.isProbablePrime(80)) continue;

%o x = n*n*3;

%o b = BigInteger.valueOf(x+1);

%o if (!b.isProbablePrime(80)) continue;

%o b = BigInteger.valueOf(x-1);

%o if (!b.isProbablePrime(80)) continue;

%o System.out.printf("%d, ", n);

%o }

%o }

%o }

%Y Cf. A173165.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Jun 08 2013

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Last modified December 6 01:25 EST 2021. Contains 349558 sequences. (Running on oeis4.)