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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

%I #4 Mar 30 2012 16:50:49

%S 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,

%T 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,

%U 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

%N 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.

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

%D 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.

%H N. J. A. Sloane, <a href="/A139767/b139767.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/A139767/a139767.txt">Fortran program for this sequence</a>

%e Let n=7, e=15: the cyclotomic cosets of 2 mod 15 are

%e C_0 := {0}

%e C_1 := {1 2 4 8}

%e C_3 := {3 6 12 9}

%e C_5 := {5 10}

%e C_7 := {-1 -2 -4 -8} == {14 13 11 7}

%e and to get an element of C_7 we must add three elements of C_1;

%e this is the worst case, so a(7) = 3.

%Y Cf. A006694.

%Y 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.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 15 2008

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)