A226109 Triangular numbers t such that t - 4, t - 2, t + 2, t + 4 are four primes.

15, 105, 1485, 18915, 666435, 2143485, 4174605, 10059855, 10440165, 28196295, 95295915, 124591005, 155064855, 171023265, 206258205, 298400235, 311737965, 347701635, 389470095, 459332895, 460424685, 498948255, 526517475, 537575655, 615496155, 645500415, 885763005, 963144105

Offset: 1

Author

Alex Ratushnyak, May 26 2013

Keywords

• nonn

Comments

Subsequence of A129752.

Proper subsequence of A226196. - Alex Ratushnyak, May 30 2013

Crossrefs

Cf. A000217, A024675, A129752, A130178, A226196.

Programs

Java

import java.math.BigInteger;
public class A226109 {
    public static void main (String[] args) {
      for (long n = 1; n < (1L << 31); n++) {
          long p2 = n * (n + 1)/2 + 2, m2 = p2 - 4;
          BigInteger b = BigInteger.valueOf(p2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(m2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(p2 + 2);
          if (!b.isProbablePrime(80)) continue;
          b = BigInteger.valueOf(m2 - 2);
          if (!b.isProbablePrime(80)) continue;
          System.out.printf("%d, ", p2 - 2);
      }
    }
}

Magma

A000217:=func; [A000217(t): t in [0..10^5] | forall{A000217(t)+i: i in [-4,-2,2,4] | IsPrime(A000217(t)+i)}]; // Bruno Berselli, May 27 2013

Mathematica

Select[Accumulate[Range[0, 70]], Union[PrimeQ[{# - 4, # - 2, # + 2, # + 4}]] == {True} &] (* Alonso del Arte, May 27 2013 *)