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Search: id:A085057
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| A085057 |
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a(n) = the smallest integer of the form a*b*c.../p*q*r..., where the numerator and the denominator contain n numbers each and a,b,c,...p,q,r... are all the integers from 1 to 2n. |
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2
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| 2, 6, 5, 70, 7, 231, 858, 1430, 12155, 46189, 176358, 676039, 104006, 44574, 1077205, 66786710, 64822395, 90751353, 353452638, 3829070245, 134564468610, 526024740930, 2287064091, 35830670759, 71661341518, 281132955186
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OFFSET
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1,1
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COMMENT
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The largest value of the ratio is C(2n,n). a(4) = 70 is the smallest as well as the largest such integer. The smallest number can arise in more than one ways. i.e. a(3) = 2*5*6/(1*3*4)=(3*4*5)/(1*2*6)=5.
Some sequence values have many representations: a(3) = 5 = 2*5*6/(1*3*4) = (3*4*5)/(1*2*6). a(n) is bounded below by the square-free part of (2n)!; and above by C(2n,n). When those bounds are equal, that is a(n); for example, a(4)=70. (cont.)
(cont.) When a(n) equals that lower bound, it is fairly easy to compute. That happens for all of the first 3400 terms, anyway. Conjecture: a(n) always equals that lower bound. - Don Reble (djr(AT)nk.ca), Jul 01 2003
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EXAMPLE
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a(3) = (2*5*6)/(1*3*4) = 5. a(5) = (1*7*8*9*10)/(2*3*4*5*6) = 7.
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CROSSREFS
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This is conjectured to be the same as A069113, they agree for at least the first 3400 terms.
Sequence in context: A085205 A094595 A069113 this_sequence A009462 A111119 A107495
Adjacent sequences: A085054 A085055 A085056 this_sequence A085058 A085059 A085060
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 26 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net) and Don Reble (djr(AT)nk.ca), Jul 01, 2003
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