A226072 Primes p such that p-1 is a triangular number and p-2 is a square.

2, 11, 11027, 16944049179227, 94511138700672573788068264540372768937231403134027

Offset: 1

Author

Alex Ratushnyak, May 25 2013

Keywords

• nonn

Comments

Intersection of A129545 and A164055.

a(6) has 106 decimal digits: 12450353555...7512227.

a(7) has 381 decimal digits: 49394105798...1431227.

Roots of corresponding squares and triangular numbers: A226074 and A226073.

Crossrefs

Cf. A226069-A226074, A129545, A164055.

Programs

Java

import java.io.*;
import java.math.BigInteger;
public class A226072 {
public static void main (String[] args) throws Exception {
  try {
    BufferedReader in = new BufferedReader(
      new FileReader(new File("b164055.txt")));
    String line;
    while ((line = in.readLine()) != null) {
      BigInteger b = new BigInteger(line.split(" ")[1]);
      b = b.add(BigInteger.ONE);
      if (b.isProbablePrime(80))
        System.out.printf("%s, ", b.toString());
    }
  } catch (Exception e) {  e.printStackTrace();  }
}
}

Mathematica

Select[Prime[Range[1500]],OddQ[Sqrt[8(#-1)+1]]&&IntegerQ[Sqrt[#-2]]&] (* The program generates the first 3 terms of the sequence. *) (* Harvey P. Dale, Jul 20 2024 *)