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

1,1

Comments

Subsequence of A129752.

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

Links

Table of n, a(n) for n=1..28.

Mathematica

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

Prog

(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<m | m*(m+1) div 2>; [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

Crossrefs

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

Sequence in context: A266503 A058085 A060218 * A264415 A319588 A344886

Adjacent sequences: A226106 A226107 A226108 * A226110 A226111 A226112

Keyword

nonn

Author

Alex Ratushnyak, May 26 2013

Status

approved