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

1,5

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)<n/2 for n>2 because the sum of all n-th roots of unity is 0.

Links

Table of n, a(n) for n=1..73.

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

Example

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

Crossrefs

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

Sequence in context: A161103 A337879 A147301 * A361231 A302098 A112779

Adjacent sequences: A108377 A108378 A108379 * A108381 A108382 A108383

Keyword

nonn

Author

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

Status

approved