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Search: id:A090907
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| A090907 |
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Group the natural numbers such that the n-th group product is a multiple of the (n-1)th group product. (1), (2),(3,4), (5,6,7,8),(9,10,11,12,13,14),(15,16,17,18,19,20,21,22,23,24,25,26),... Sequence contains ratio of successive products. |
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+0
5
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| 2, 6, 140, 1287, 2139552000, 2949442889323392, 322686644032484531917367528014184448000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: For n > 4 the last term of the n-th group is 2p where p is the largest prime in the (n-1)th group. And these are the Bertrand primes.
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EXAMPLE
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a(1)=(2!/1!)*(0!/1!)
a(2)=(4!/2!)*(1!/2!)
a(3)=(8!/4!)*(2!/4!)
a(4)=(14!/8!)*(4!/8!)
a(5)=(26!/14!)*(8!/14!)
a(6)=(46!/26!)*(14!/26!)
For n>=6 we have a(n)= ((2*A006992(n))!/(2*A006992(n-1))!)*((2*A006992(n-2))!/(2*A006992(n-1))!), verified for 4<n<21
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CROSSREFS
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Cf. A090904, A090905, A090906.
Sequence in context: A060001 A101753 A156515 this_sequence A159478 A047937 A027731
Adjacent sequences: A090904 A090905 A090906 this_sequence A090908 A090909 A090910
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 13 2003
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EXTENSIONS
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Edited by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 05 2004
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