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Search: id:A108380
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| A108380 |
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Least number of distinct n-th roots of unity summing to the smallest possible nonzero magnitude. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 5, 5, 6, 6, 4, 5, 5, 5, 7, 7, 10, 5, 8, 7, 12, 7, 10, 9, 14, 13, 11, 7, 14, 11, 17, 9, 18, 14, 18, 9, 19, 12, 17, 15, 14, 14, 22, 15, 16, 20, 20, 17, 18, 22, 23, 17, 24, 19, 26, 21, 29, 18, 26, 19, 26, 31, 30, 27, 31, 17, 32, 23, 34
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Myerson writes about the unsolved problem of finding a good lower bound on the least magnitude as a function of n. Note that a(n)<n/2 for n>2 because the sum of all n-th roots of unity is 0.
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REFERENCES
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Gerald Myerson, How small can a sum of roots of unity be?, Amer. Math. Monthly, Vol. 93 (1986), No. 6, 457-459.
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LINKS
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T. D. Noe, Plot of the least magnitude for n<=73
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EXAMPLE
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a(8)=3 because the least nonzero magnitude is sqrt(2)-1, which is the sum of three 8th roots of unity.
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CROSSREFS
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Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).
Sequence in context: A119994 A029167 A147301 this_sequence A112779 A029201 A071283
Adjacent sequences: A108377 A108378 A108379 this_sequence A108381 A108382 A108383
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 01 2005, extended Jun 04 2005
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