A173042 - OEIS

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: 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.

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

(list; graph; refs; listen; history; text; internal format)

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 Four-Square 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