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Search: id:A084109
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| A084109 |
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n is congruent to 1 (mod 4) and is not the sum of two squares. |
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+0
5
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| 21, 33, 57, 69, 77, 93, 105, 129, 133, 141, 161, 165, 177, 189, 201, 209, 213, 217, 237, 249, 253, 273, 285, 297, 301, 309, 321, 329, 341, 345, 357, 381, 385, 393, 413, 417, 429, 437, 453, 465, 469, 473, 489, 497
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Alternatively, n is congruent to 1 (mod 4) such that no prime factor in the square-free part of n is congruent to 3 (mod 4).
Applications to the theory of optimal weighing designs and maximal determinants: An (n+1) X (n+1) conference matrix is impossible.
The upper bound of Ehlich/Wojtas on the determinant of a (0,1) matrix of order congruent to 1 (mod 4) cannot be achieved for n X n matrices.
The bound of Ehlich/Wojtas on the determinant of a (-1,1) matrix of order congruent to 2 (mod 4) cannot be achieved for (n+1) X (n+1) matrices.
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REFERENCES
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H. Ehlich, Determinantenabschaetzungen fuer binaere Matrizen, Math. Z. 83 (1964) 123-132.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 56.
D. Raghavarao, Some aspects of weighing designs, Ann. Math. Stat. 31 (1960) 878-884.
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MATHEMATICA
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a[m_] := Complement[Range[1, m, 4], Union[Flatten[Table[j^2+k^2, {j, 1, Sqrt[m], 2}, {k, 0, Sqrt[m], 2}]]]]
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CROSSREFS
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Cf. A000952, A003432, A003433.
Sequence in context: A141249 A026068 A070006 this_sequence A016105 A032603 A128283
Adjacent sequences: A084106 A084107 A084108 this_sequence A084110 A084111 A084112
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KEYWORD
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easy,nonn
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AUTHOR
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Will Orrick (worrick(AT)indiana.edu), Jun 18 2003
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