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

0,5

Links

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

Example

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.

Mathematica

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

Prog

(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] + ", ");
}

Crossrefs

Cf. A273190.

Sequence in context: A307968 A338501 A242464 * A375467 A373183 A351776

Adjacent sequences: A273182 A273183 A273184 * A273186 A273187 A273188

Keyword

easy,nonn

Author

Alec Jones, May 17 2016

Status

approved