OFFSET
1,3
COMMENTS
A disjoint covering system is a system of n congruences x == a_i (mod m_i) such that every integer is a solution to exactly one of the congruences. This sequence counts them up to "shift"; that is, two systems are the same if we can turn one into another by subtracting a constant from x.
LINKS
I. P. Goulden, Andrew Granville, L. Bruce Richmond, and Jeffrey Shallit, Natural exact covering systems and the reversion of the Möbius series, Ramanujan J. (2019) Vol. 50, 211-235.
Břetislav Novák and Štefan Znám, Disjoint Covering Systems, The American Mathematical Monthly, Vol. 81, No. 1 (1974), 42-45.
Wikipedia, Covering system.
EXAMPLE
For n = 3 there are three disjoint covering systems:
(a) x == 0 (mod 3), x == 1 (mod 3), x == 2 (mod 3)
(b) x == 0 (mod 2), x == 1 (mod 4), x == 3 (mod 4)
(c) x == 1 (mod 2), x == 0 (mod 4), x == 2 (mod 4)
but (b) and (c) are equivalent under shift.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Nov 06 2017
STATUS
approved