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A275489 Most consecutive numbers that can be covered with arithmetic progressions of differences 2i+1, 1<=i<=n. 1
1, 2, 4, 6, 10, 13, 17, 22, 30, 38, 45, 53, 63, 74, 83, 96, 112, 128, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Erdos and Selfridge conjecture that there is no covering system whose moduli are distinct odd integers > 1. This is equivalent to saying that a(n) is finite for all n.

LINKS

Table of n, a(n) for n=1..19.

Wikipedia, Covering system.

EXAMPLE

[1,2,3,4] can be covered by the arithmetic progressions 3k+1, 5k+2 and 7k+3 but [1,2,3,4,5] can't be covered by three arithmetic progressions with differences 3, 5 and 7, so  a(3) = 4.

CROSSREFS

Sequence in context: A233556 A087148 A297531 * A153817 A309616 A267452

Adjacent sequences:  A275486 A275487 A275488 * A275490 A275491 A275492

KEYWORD

nonn,more

AUTHOR

Robert Israel, Jul 29 2016

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)