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%I #6 Mar 30 2012 17:23:02
%S 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,
%T 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,
%U 3,3,4,2,4,2,3,4,3,3,4,2,1,4,3,4,2,3,4
%N Least number of squares required when writing n as a sum of squares with the smallest square as large as possible.
%C 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.
%H T. D. Noe, <a href="/A191091/b191091.txt">Table of n, a(n) for n = 1..1000</a>
%e The sum for 30 gives the first sum having 5 terms: 4 + 4 + 4 + 9 + 9.
%t Table[s=DeleteCases[#, 0]& /@ PowersRepresentations[n,11,2]; t=Last[Union[First /@ Union /@ s]]; Min @@ Length /@ Select[s, #[[1]] == t &], {n, 100}]
%Y Cf. A191090, A193018.
%K nonn
%O 1,2
%A _T. D. Noe_, Jul 21 2011
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