A273185 Start with a(0) = 0. Thereafter a(n) is the number of m < n with the property that a(m) + n is a perfect square.

0, 1, 0, 1, 2, 0, 0, 1, 3, 4, 0, 0, 1, 1, 1, 6, 6, 0, 0, 2, 0, 1, 1, 2, 8, 9, 0, 1, 1, 0, 2, 0, 1, 1, 4, 12, 12, 2, 0, 0, 1, 1, 0, 2, 0, 2, 1, 7, 15, 17, 0, 0, 2, 0, 0, 1, 1, 1, 2, 0, 2, 1, 10, 19, 22, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 14

Offset: 0

Author

Alec Jones, May 17 2016

Keywords

• easy
• nonn

Examples

			a(3) = 1 because 3 + a(1) is a perfect square.
a(4) = 2 because 4 + a(0) and 4 + a(2) are perfect squares.
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A273190.

Programs

Java

int n = 1000;
int[] terms = new int[n];
for (int i = 0; i < n; i++) {
     for (int j = 0; j < i; j++) {
          if (Math.sqrt(i+terms[j]) == Math.floor(Math.sqrt(i+terms[j]))) {
               terms[i]++;
          }
     }
     System.out.print(terms[i] + ", ");
}

Mathematica

a = {0}; Do[AppendTo[a, Count[a + n, k_ /; IntegerQ@ Sqrt@ k]], {n, 79}]; a (* Michael De Vlieger, May 25 2016 *)