A108380 Least number of distinct n-th roots of unity summing to the smallest possible nonzero magnitude.

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

Offset: 1

Author

T. D. Noe, Jun 01 2005, extended Jun 04 2005

Keywords

• nonn

Comments

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)2 because the sum of all n-th roots of unity is 0.

Examples

			a(8)=3 because the least nonzero magnitude is sqrt(2)-1, which is the sum of three 8th roots of unity.
		

Links

• Gerald Myerson, How small can a sum of roots of unity be?, Amer. Math. Monthly, Vol. 93 (1986), No. 6, 457-459.
• T. D. Noe, Plot of the least magnitude for n<=81

Crossrefs

Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).