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%I #8 Mar 12 2017 16:43:40
%S 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,
%T 7,14,11,17,9,18,14,18,9,19,12,17,15,14,14,22,15,16,20,20,17,18,22,23,
%U 17,24,19,26,21,29,18,26,19,26,31,30,27,31,17,32,23,34
%N Least number of distinct n-th roots of unity summing to the smallest possible nonzero magnitude.
%C 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.
%H Gerald Myerson, <a href="http://www.jstor.org/stable/2323469">How small can a sum of roots of unity be?</a>, Amer. Math. Monthly, Vol. 93 (1986), No. 6, 457-459.
%H T. D. Noe, <a href="http://www.sspectra.com/math/A108380.gif">Plot of the least magnitude for n<=81</a>
%e a(8)=3 because the least nonzero magnitude is sqrt(2)-1, which is the sum of three 8th roots of unity.
%Y Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).
%K nonn
%O 1,5
%A _T. D. Noe_, Jun 01 2005, extended Jun 04 2005
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