A139767 Let e = 2n+1; consider the cyclotomic cosets C_i of 2 mod e; a(n) = maximal value of minimal number of copies of C_1 needed to add together to get any coset C_i.

1, 1, 2, 2, 1, 1, 3, 2, 1, 3, 2, 2, 2, 1, 4, 3, 3, 1, 2, 2, 2, 4, 2, 3, 3, 1, 2, 3, 1, 1, 5, 3, 1, 3, 2, 3, 4, 3, 2, 2, 1, 4, 2, 3, 3, 5, 2, 2, 3, 1, 2, 4, 1, 2, 2, 2, 3, 3, 3, 2, 3, 2, 6, 4, 1, 3, 4, 2, 1, 3, 2, 3, 3, 1, 3, 4, 5, 2, 2, 3, 1, 4, 2, 2, 3, 1, 3, 3, 1, 1, 2, 3, 2, 6, 2, 2, 4, 1, 2

Offset

1,3

Comments

C_i = {i, 2i, 4i, ... } reduced mod e.

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland/Elsevier, 1977; see p. 104 for definition of cyclotomic coset.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Fortran program for this sequence

Example

Let n=7, e=15: the cyclotomic cosets of 2 mod 15 are
C_0 := {0}
C_1 := {1 2 4 8}
C_3 := {3 6 12 9}
C_5 := {5 10}
C_7 := {-1 -2 -4 -8} == {14 13 11 7}
and to get an element of C_7 we must add three elements of C_1;
this is the worst case, so a(7) = 3.

Crossrefs

Cf. A006694.

Records occur when e is of the form 2^j - 1. Sequence is 1 iff e is in A001122. A140364 lists e such that the sequence is 2.

Sequence in context: A047000 A288915 A175062 * A207822 A343068 A370489

Adjacent sequences: A139764 A139765 A139766 * A139768 A139769 A139770

Keyword

nonn

Author

N. J. A. Sloane, Jun 15 2008

Status

approved