The On-Line Encyclopedia of Integer Sequences (OEIS)

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A275489

Most consecutive numbers that can be covered with arithmetic progressions of differences 2i+1, 1<=i<=n.
(history; published version)

#7 by N. J. A. Sloane at Fri Jul 29 21:19:03 EDT 2016

STATUS

editing

approved

#6 by N. J. A. Sloane at Fri Jul 29 21:19:00 EDT 2016

KEYWORD

nonn,changed,more

STATUS

proposed

editing

#5 by Omar E. Pol at Fri Jul 29 20:55:00 EDT 2016

STATUS

editing

proposed

#4 by Omar E. Pol at Fri Jul 29 20:54:56 EDT 2016

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.

STATUS

proposed

editing

#3 by Robert Israel at Fri Jul 29 20:12:56 EDT 2016

STATUS

editing

proposed

Discussion

Fri Jul 29

20:53

Omar E. Pol: The sequence needs more keywords.

#2 by Robert Israel at Fri Jul 29 20:07:59 EDT 2016

NAME

allocated for Robert IsraelMost consecutive numbers that can be covered with arithmetic progressions of differences 2i+1, 1<=i<=n.

DATA

1, 2, 4, 6, 10, 13, 17, 22, 30, 38, 45, 53, 63, 74, 83, 96, 112, 128, 145

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

Wikipedia, <a href="https://en.wikipedia.org/wiki/Covering_system">Covering system</a>.

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.

KEYWORD

allocated

nonn

AUTHOR

Robert Israel, Jul 29 2016

STATUS

approved

editing

#1 by Robert Israel at Fri Jul 29 20:07:59 EDT 2016

NAME

allocated for Robert Israel

KEYWORD

allocated

STATUS

approved