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A112687
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Numbers n that can not be decomposed into the sum of at most 4 square numbers when using the following 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. The sequence presented is of those numbers where n is not 0 when this algorithm ends.
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2
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23, 32, 43, 48, 56, 61, 71, 76, 79, 88, 93, 96, 107, 112, 115, 119, 128, 133, 136, 140, 143, 151, 156, 159, 163, 166, 167, 176, 181, 184, 188, 191, 192, 203, 208, 211, 215, 218, 219, 224, 232, 237, 240, 244, 247, 248, 253, 263, 268, 271, 275, 278, 279, 284
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Found while writing a program to decompose integers as sums of four square numbers (following Lagrange's Four-Square Theorem).
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LINKS
| Eric Weisstein's World of Mathematics, Lagrange's Four-Square Theorem
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EXAMPLE
| 23 is the first number that cannot be decomposed because 16+4+1+1 falls short by one.
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PROG
| (Other) % Matlab code for sequence A112687 % Luis F.B.A. Alexandre, 2010-02-08 for n=1:312 a=n; i=1; while(i<5 & n~=0) j=1; while(j*j<=n) j=j+1; end; n=n-(j-1)*(j-1); i=i+1; end; if(n~=0) disp(a); end; end; [From Luis F.B.A. Alexandre (lfbaa(AT)di.ubi.pt), Feb 08 2010]
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CROSSREFS
| Sequence in context: A093477 A070664 A096083 * A107282 A039410 A043233
Adjacent sequences: A112684 A112685 A112686 * A112688 A112689 A112690
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KEYWORD
| nonn
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AUTHOR
| Luis F.B.A. Alexandre (lfbaa(AT)di.ubi.pt), Dec 31 2005
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EXTENSIONS
| Included terms where the final value of n is larger than 1. The fact that some terms might be missing was noted by Alonso Del Arte (alonso.delarte(AT)gmail.com) on 2010-02-07. Luis F.B.A. Alexandre (lfbaa(AT)di.ubi.pt), Feb 08 2010
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