

A173042


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: 1find the largest square s smaller than n; 2n=ns 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.


0



48, 71, 96, 112, 128, 143, 163, 176, 191, 192, 208, 211, 224, 244, 248, 268, 288, 304, 308, 311, 312, 317, 331, 336, 352, 356, 376, 380, 384, 422, 428, 431, 432, 439, 448, 456, 460, 463, 496, 512, 516, 536, 544, 551, 560, 568, 571, 572, 599, 604, 607, 608
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OFFSET

1,1


COMMENTS

This is a subsequence of A112687.


LINKS

Table of n, a(n) for n=1..52.
Eric Weisstein's World of Mathematics, Lagrange's FourSquare Theorem


EXAMPLE

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.


CROSSREFS

Cf. A112687
Sequence in context: A043157 A039334 A043937 * A309933 A124309 A112058
Adjacent sequences: A173039 A173040 A173041 * A173043 A173044 A173045


KEYWORD

nonn


AUTHOR

Luis F.B.A. Alexandre (lfbaa(AT)di.ubi.pt), Feb 08 2010


STATUS

approved



