OFFSET
1,3
COMMENTS
A disjoint covering system or DCS (also called "exact covering system" or ECS) is a system of n congruences such that every integer belongs to exactly one of the congruences.
This sequence agrees with A050385 on the first 12 terms, but differs at a(13).
REFERENCES
S. Porubsky and J. Schönheim, Covering systems of Paul Erdös: past, present and future, in Paul Erdös and his Mathematics, Vol. I, Bolyai Society Mathematical Studies 11 (2002), 581-627.
LINKS
I. P. Goulden, L. B. Richmond, and J. Shallit, Natural exact covering systems and the reversion of the Möbius series, arXiv:1711.04109v3 [math.NT], revision of Dec 12 2017
EXAMPLE
For n = 3 the a(3) = 3 DCS are
(i) x == 0 (mod 3), x == 1 (mod 3), x == 2 (mod 3)
(ii) x == 0 (mod 2), x == 1 (mod 4), x == 3 (mod 4)
(iii) x == 1 (mod 2), x == 0 (mod 4), x == 2 (mod 4)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Dec 07 2017
STATUS
approved