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
Offset: 1
Keywords
Examples
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.
Links
- Eric Weisstein's World of Mathematics, Lagrange's Four-Square Theorem
Crossrefs
Cf. A112687
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