A191091 Least number of squares required when writing n as a sum of squares with the smallest square as large as possible.

1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 1, 3, 2, 3, 2, 4, 3, 4, 3, 1, 4, 3, 4, 2, 5, 4, 2, 3, 2, 5, 1, 4, 3, 6, 2, 2, 4, 3, 3, 2, 5, 4, 3, 1, 2, 5, 2, 2, 3, 6, 3, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 3, 3, 3, 3, 4, 2, 4, 2, 3, 4, 3, 3, 4, 2, 1, 4, 3, 4, 2, 3, 4

Offset: 1

Author

T. D. Noe, Jul 21 2011

Keywords

• nonn

Comments

The smallest value in the sum is A191090. All sums have at most 6 terms for n <= 1000. Is this the largest possible value? For n up to 1000, only 39, 55, 143, 543, and 564 need 6 terms.

Examples

			The sum for 30 gives the first sum having 5 terms: 4 + 4 + 4 + 9 + 9.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A191090, A193018.

Programs

Mathematica

Table[s=DeleteCases[#, 0]& /@ PowersRepresentations[n,11,2]; t=Last[Union[First /@ Union /@ s]]; Min @@ Length /@ Select[s, #[[1]] == t &], {n, 100}]