|
%I #1 Jun 01 2010 03:00:00
%S 48,71,96,112,128,143,163,176,191,192,208,211,224,244,248,268,288,304,
%T 308,311,312,317,331,336,352,356,376,380,384,422,428,431,432,439,448,
%U 456,460,463,496,512,516,536,544,551,560,568,571,572,599,604,607,608
%N Numbers n that cannot be decomposed into the sum of up to 4 squares using the following algorithm: If n is not decomposable using the algorithm: [Repeat the following 2 steps 4 times: 1-find the largest square s smaller than n; 2-n=n-s Numbers that can be decomposed yield final values of n=0.] then choose the first square as the second largest square smaller than n and try finding the remaining up to 3 squares using the 2 steps of the algorithm in brackets.
%C This is a subsequence of A112687.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LagrangesFour-SquareTheorem.html">Lagrange's Four-Square Theorem</a>
%e For n=48: it is not decomposable using the algorithm in brackets, so instead of using the first s=36 we choose s=25 (the second largest). So the attempt to decompose 48 is now 5*5+(up to more 3 squares which will be found using steps 1 and 2 of the algorithm in brackets). This yields 5*5+4*4+2*2+1*1 which does not give 48 hence it is not decomposable using this algorithm.
%Y Cf. A112687
%K nonn
%O 1,1
%A Luis F.B.A. Alexandre (lfbaa(AT)di.ubi.pt), Feb 08 2010
|
