Search: id:A058989
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%I A058989
%S A058989 1,3,5,9,13,21,25,33,39,45,57,65,73,89,99,105,117,131,151,173,189,
%T A058989 199,215,233,257,263,281,299,311,329,353,377,387,413,431,449,475,
%U A058989 491,509,537,549,573,599,615,641,657,685,717,741
%N A058989 Largest number of consecutive integers such that each is divisible by 
               a prime <= the n-th prime.
%C A058989 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.
%C A058989 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
%D A058989 Dickson, L. E., History of the Theory of Numbers, Vol. 1, p. 439, Chelsea, 
               1952.
%D A058989 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.
%e A058989 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.
%Y A058989 This sequence is the same as A048670 - 1. See that entry for additional 
               information.
%Y A058989 Cf. A000040.
%Y A058989 Sequence in context: A106607 A007042 A076274 this_sequence A049691 A136252 
               A141325
%Y A058989 Adjacent sequences: A058986 A058987 A058988 this_sequence A058990 A058991 
               A058992
%K A058989 nice,nonn
%O A058989 1,2
%A A058989 Jud McCranie (j.mccranie(AT)comcast.net), Jan 16 2001
%E A058989 Laison and Schick reference from Parthasarathy Nambi (PachaNambi(AT)yahoo.com), 
               Oct 19 2007
%E A058989 More terms from Max Alekseyev, Feb 07 2008

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