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Search: id:A160560
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| A160560 |
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Almost minimal covering numbers |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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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.
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LINKS
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Pace P. Nielsen, A movie explaning covering systems.
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EXAMPLE
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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.
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PROGRAM
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(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.
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CROSSREFS
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Cf. A160559
Sequence in context: A073696 A058602 A133808 this_sequence A093109 A070034 A064408
Adjacent sequences: A160557 A160558 A160559 this_sequence A160561 A160562 A160563
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KEYWORD
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nonn
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AUTHOR
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Matthijs Coster (sequences(AT)matcos.nl), May 19 2009
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