A215539 First square that can be represented as the sum of n nonzero squares.

1, 25, 9, 4, 16, 9, 16, 16, 9, 16, 25, 36, 16, 25, 36, 16, 25, 36, 25, 36, 36, 25, 49, 36, 25, 49, 36, 36, 49, 36, 49, 49, 36, 49, 49, 36, 49, 49, 64, 49, 49, 64, 49, 64, 64, 49, 64, 64, 49, 64, 81, 64, 64, 81, 64, 64, 81, 64, 81, 81, 64, 81, 81, 64, 81, 81

Offset: 1

Author

Jon Perry, Aug 15 2012

Keywords

• nonn

Examples

			a(1) =  1 = 1^2.
a(2) = 25 = 3^2 + 4^2.
a(3) =  9 = 1^2 + 2*2^2.
a(4) =  4 = 4*1^2.
a(5) = 16 = 3*1^2 + 2^2 + 3^2.
a(6) =  9 = 5*1^2 + 2^2.
a(7) = 16 = 4*1^2 + 3*2^2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Maple

b:= proc(n, i, t) option remember; n>=t and (n=t or
      (i>0 and (b(n, i-1, t) or i^2<=n and b(n-i^2, i, t-1))))
    end:
a:= proc(n) option remember; local k;
      for k while not b(k^2, k, n) do od; k^2
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 26 2012

Mathematica

b[n_, i_, t_] := b[n, i, t] = n >= t && (n == t || (i > 0 && (b[n, i - 1, t] || i^2 <= n && b[n - i^2, i, t - 1])));
a[n_] := a[n] = Module[{k}, For[k = 1, !b[k^2, k, n], k++]; k^2];
Array[a, 100] (* Jean-François Alcover, Nov 22 2020, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Aug 26 2012