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Search: id:A058989
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| A058989 |
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Largest number of consecutive integers such that each is divisible by a prime <= the n-th prime. |
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+0
3
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| 1, 3, 5, 9, 13, 21, 25, 33, 39, 45, 57, 65, 73, 89, 99, 105, 117, 131, 151, 173, 189, 199, 215, 233, 257, 263, 281, 299, 311, 329, 353, 377, 387, 413, 431, 449, 475, 491, 509, 537, 549, 573, 599, 615, 641, 657, 685, 717, 741
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Marty Weissman conjectured that a(n)=2q-1, where q is the largest prime smaller than the n-th prime. The conjecture holds for the first few terms, but then a(n) is larger than 2q-1. Phil Carmody proved a(n)>=2q-1. Terms were calculated by Weissman, Carmody and McCranie.
a(n)=A048670(n) - 1, A049300(n) is the smallest value of the mentioned consecutive integers. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 14 2003
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REFERENCES
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Dickson, L. E., History of the Theory of Numbers, Vol. 1, p. 439, Chelsea, 1952.
J. D. Laison and M. Schick, "Seeing Dots: Visibility of Lattice Points", Mathematics Magazine, Vol. 80 (2007), pp. 274-282. See page 281 reference 13.
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EXAMPLE
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The 4th prime is 7. Nine is the maximum number of consecutive integers such that each is divisible by 2, 3, 5 or 7. (Example: 2 through 10) So a(4)=9.
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CROSSREFS
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This sequence is the same as A048670 - 1. See that entry for additional information.
Cf. A000040.
Sequence in context: A106607 A007042 A076274 this_sequence A049691 A136252 A141325
Adjacent sequences: A058986 A058987 A058988 this_sequence A058990 A058991 A058992
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KEYWORD
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nice,nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net), Jan 16 2001
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EXTENSIONS
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Laison and Schick reference from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Oct 19 2007
More terms from Max Alekseyev, Feb 07 2008
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