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

1,2

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A191090, A193018.

Sequence in context: A194050 A316340 A002828 * A098066 A096436 A053610

Adjacent sequences: A191088 A191089 A191090 * A191092 A191093 A191094

Keyword

nonn

Author

T. D. Noe, Jul 21 2011

Status

approved