cp's OEIS Frontend

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

%I A226072 #8 Jul 20 2024 19:20:54
%S A226072 2,11,11027,16944049179227,
%T A226072 94511138700672573788068264540372768937231403134027
%N A226072 Primes p such that p-1 is a triangular number and p-2 is a square.
%C A226072 Intersection of A129545 and A164055.
%C A226072 a(6) has 106 decimal digits: 12450353555...7512227.
%C A226072 a(7) has 381 decimal digits: 49394105798...1431227.
%C A226072 Roots of corresponding squares and triangular numbers: A226074 and A226073.
%t A226072 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 *)
%o A226072 (Java)
%o A226072 import java.io.*;
%o A226072 import java.math.BigInteger;
%o A226072 public class A226072 {
%o A226072 public static void main (String[] args) throws Exception {
%o A226072   try {
%o A226072     BufferedReader in = new BufferedReader(
%o A226072       new FileReader(new File("b164055.txt")));
%o A226072     String line;
%o A226072     while ((line = in.readLine()) != null) {
%o A226072       BigInteger b = new BigInteger(line.split(" ")[1]);
%o A226072       b = b.add(BigInteger.ONE);
%o A226072       if (b.isProbablePrime(80))
%o A226072         System.out.printf("%s, ", b.toString());
%o A226072     }
%o A226072   } catch (Exception e) {  e.printStackTrace();  }
%o A226072 }
%o A226072 }
%Y A226072 Cf. A226069-A226074, A129545, A164055.
%K A226072 nonn
%O A226072 1,1
%A A226072 _Alex Ratushnyak_, May 25 2013