login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A057555 A075532

Adjacent sequences:  A139764 A139765 A139766 * A139768 A139769 A139770

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 15 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)