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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.

%I A139767 #4 Mar 30 2012 16:50:49
%S A139767 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 A139767 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 A139767 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 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.
%C A139767 C_i = {i, 2i, 4i, ... } reduced mod e.
%D A139767 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 A139767 N. J. A. Sloane, <a href="/A139767/b139767.txt">Table of n, a(n) for n = 1..1000</a>
%H A139767 N. J. A. Sloane, <a href="/A139767/a139767.txt">Fortran program for this sequence</a>
%e A139767 Let n=7, e=15: the cyclotomic cosets of 2 mod 15 are
%e A139767 C_0 := {0}
%e A139767 C_1 := {1 2 4 8}
%e A139767 C_3 := {3 6 12 9}
%e A139767 C_5 := {5 10}
%e A139767 C_7 := {-1 -2 -4 -8} == {14 13 11 7}
%e A139767 and to get an element of C_7 we must add three elements of C_1;
%e A139767 this is the worst case, so a(7) = 3.
%Y A139767 Cf. A006694.
%Y A139767 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 A139767 nonn
%O A139767 1,3
%A A139767 _N. J. A. Sloane_, Jun 15 2008