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

1,2

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A307179 A065910 A096521 * A224490 A226224 A181763

Adjacent sequences: A215536 A215537 A215538 * A215540 A215541 A215542

Keyword

nonn

Author

Jon Perry, Aug 15 2012

Extensions

More terms from Alois P. Heinz, Aug 26 2012

Status

approved