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A351061
Smallest positive integer whose square can be written as the sum of n positive perfect squares.
2
1, 5, 3, 2, 4, 3, 4, 4, 3, 4, 5, 6, 4, 5, 6, 4, 5, 6, 5, 6, 6, 5, 7, 6, 5, 7, 6, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 8, 7, 7, 8, 7, 8, 8, 7, 8, 8, 7, 8, 9, 8, 8, 9, 8, 8, 9, 8, 9, 9, 8, 9, 9, 8, 9, 9, 9, 10, 9, 9, 10, 9, 9, 10, 9, 10, 10, 9, 10, 10, 9, 10, 10, 10
OFFSET
1,2
COMMENTS
Shortest possible integer length of the diagonal of an n-dimensional hyperrectangle where each edge has a positive integer length.
LINKS
FORMULA
a(n) = sqrt(A215539(n)). - Jinyuan Wang, Jan 30 2022
EXAMPLE
a(1) = 1 because 1^2 = 1^2.
a(2) = 5 because 5^2 = 3^2 + 4^2.
a(3) = 3 because 3^2 = 1^2 + 2*(2^2).
a(4) = 2 because 2^2 = 4*(1^2).
a(5) = 4 because 4^2 = 3*(1^2) + 2^2 + 3^2.
a(6) = 3 because 3^2 = 5*(1^2) + 2^2.
a(7) = 4 because 4^2 = 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
end:
seq(a(n), n=1..100); # Alois P. Heinz, Jan 31 2022
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];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)
CROSSREFS
Cf. A215539.
Sequence in context: A372389 A040022 A165100 * A159935 A165102 A294568
KEYWORD
nonn
AUTHOR
Lee A. Newberg, Jan 30 2022
EXTENSIONS
More terms from Jinyuan Wang, Jan 30 2022
STATUS
approved