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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
6, 2100, 20586, 669054, 745590, 6556122, 9317496, 10190796, 15648732, 18215196, 25561410, 35613990, 36710652, 38649066, 41124594, 41711874, 46576524, 48701400, 49406358, 59278296, 70038948, 74993808, 75553092, 83606418, 84182154, 88000374, 92527764, 98969052, 100691976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..29.

MATHEMATICA

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 *)

PROG

(Java)

import java.math.BigInteger;

public class A226461 {

    public static void main (String[] args) {

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

          long x = n*n*5;

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

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

          b = BigInteger.valueOf(x-1);

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

          x = n*n*2;

          b = BigInteger.valueOf(x+1);

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

          b = BigInteger.valueOf(x-1);

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

          x = n*n*3;

          b = BigInteger.valueOf(x+1);

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

          b = BigInteger.valueOf(x-1);

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

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

      }

    }

}

CROSSREFS

Cf. A173165.

Sequence in context: A004817 A089535 A059081 * A172943 A182789 A056048

Adjacent sequences:  A226458 A226459 A226460 * A226462 A226463 A226464

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Jun 08 2013

STATUS

approved

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Last modified October 25 20:31 EDT 2021. Contains 348256 sequences. (Running on oeis4.)