A226072 - OEIS

%I #8 Jul 20 2024 19:20:54

%S 2,11,11027,16944049179227,

%T 94511138700672573788068264540372768937231403134027

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

%C Intersection of A129545 and A164055.

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

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

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

%t 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 (Java)

%o import java.io.*;

%o import java.math.BigInteger;

%o public class A226072 {

%o public static void main (String[] args) throws Exception {

%o   try {

%o     BufferedReader in = new BufferedReader(

%o       new FileReader(new File("b164055.txt")));

%o     String line;

%o     while ((line = in.readLine()) != null) {

%o       BigInteger b = new BigInteger(line.split(" ")[1]);

%o       b = b.add(BigInteger.ONE);

%o       if (b.isProbablePrime(80))

%o         System.out.printf("%s, ", b.toString());

%o     }

%o   } catch (Exception e) {  e.printStackTrace();  }

%o }

%o }

%Y Cf. A226069-A226074, A129545, A164055.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, May 25 2013