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Search: id:A072881
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| A072881 |
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a(1)=a(2)=a(3)=1; for n>3, a(n)=(a(n-1)*a(n-2)+a(n-1)+a(n-2))/a(n-3). |
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+0
2
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| 1, 1, 1, 3, 7, 31, 85, 393, 1093, 5071, 14119, 65523, 182449, 846721, 2357713, 10941843, 30467815, 141397231, 393723877, 1827222153, 5087942581, 23612490751, 65749529671, 305135157603, 849655943137, 3943144558081
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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What accounts for the high proportion of semiprimes in this sequence? Primes: 3, 7, 31, 1093, 846721, 393723877, ... Semiprimes: 85 = 5 * 17 393 = 3 * 131 5071 = 11 * 461 14119 = 7 * 2017 65523 = 3 * 21841 182449 = 43 * 4243 5087942581 = 11113 * 457837 849655943137 = 17 * 49979761361 3943144558081 = 31 * 127198211551 - Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 04 2005
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LINKS
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P. Heideman and E. Hogan, A new family of Somos-like recurrences.
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FORMULA
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Both sequences u=(a(2n-1))_{n>0} and u=(a(2n))_{n>0} satisfy the order 3 linear recursion : u(n)=14u(n-1)-14u(n-2)+u(n-3)
a(2*n-1)=ceil((1/11)*sqrt(1002/5-78*sqrt(33/5))*(sqrt(15)/2+sqrt(11)/ 2)^(2*n-1))
a(2*n)=ceil((1/11)*(13-sqrt(165))*(sqrt(15)/2+sqrt(11)/2)^(2*n))
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CROSSREFS
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Sequence in context: A109140 A088193 A091383 this_sequence A132153 A002357 A105765
Adjacent sequences: A072878 A072879 A072880 this_sequence A072882 A072883 A072884
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 28 2002, revised Feb 03 2005
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