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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.

+0
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; listen)

	OFFSET	`1,3`
	COMMENT	`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: A059674 A117545 A047000 this_sequence A057555 A075532 A050176` `Adjacent sequences: A139764 A139765 A139766 this_sequence A139768 A139769 A139770`
	KEYWORD	`nonn`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), Jun 15 2008`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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