|
| |
|
|
A160560
|
|
Almost minimal covering numbers
|
|
1
| |
|
|
2, 4, 6, 8, 16, 18, 30, 32, 40, 54, 64, 126, 128, 150, 162, 200, 224, 256, 486, 512, 750, 882, 1000, 1024, 1458, 1568, 1782, 1950, 2048, 2600, 2912, 3750, 4096, 4374, 5000, 5632
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a covering system. Let N be the gcd of these moduli. If modulo N one number is uncovered then we speak about an almost minimal covering number.
|
|
|
REFERENCES
| Donald Jason Gibson, A covering system with least modulus 25, Math. Comp. 78, (2009), 1127-1146.
Pace P. Nielsen, A covering system whose smallest modulus is 40, Journal of Number Theory 129, (2009), 640-666.
|
|
|
LINKS
| Pace P. Nielsen, A movie explaining covering systems.
|
|
|
EXAMPLE
| 30 is an almost minimal covering number since 1 mod 2; 2 mod 3; 4 mod 5; 4 mod 6; 8 mod 10; 12 mod 15 and 6 mod 30 covers all numbers modulo 30 exept 30-folds.
|
|
|
PROG
| (Other) We denote by T(N) the number of divisors of N. We denote by R(N) the number of uncovered numbers modulo N. Suppose N=p^k.M, where gcd(p, M)=1, p prime, R(M) = 1 and T(M) = p-1 then R(N) = 1 as well. R(p) = p-1.
|
|
|
CROSSREFS
| Cf. A160559
Sequence in context: A073696 A058602 A133808 * A093109 A070034 A064408
Adjacent sequences: A160557 A160558 A160559 * A160561 A160562 A160563
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Matthijs Coster (sequences(AT)matcos.nl), May 19 2009
|
| |
|
|
