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A069214
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Let u(n,k) be the recursion defined by u(n,1)=1 u(n,2)=2 u(n,3)=n and u(n,k+3)=(u(n,k+2)+u(n,k+1))/u(n,k) if u(n,k) divides u(n,k+2)+u(n,k+1) u(n,k+3)=u(n,k) otherwise. Then u(n,k) is periodic and a(n)=Max(u(n,k) k=1,2,3,4.....).
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5, 4, 5, 6, 8, 8, 11, 10, 14, 12, 17, 14, 20, 16, 23, 18, 26, 20, 29, 22, 32, 24, 35, 26, 38, 28, 41, 30, 44, 32, 47, 34, 50, 36, 53, 38, 56, 40, 59, 42, 62, 44, 65, 46, 68, 48, 71, 50, 74, 52, 77, 54, 80, 56, 83, 58, 86, 60, 89, 62, 92, 64, 95, 66, 97, 68, 100, 70, 103, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Let p(n) denotes the length of the period of u(n,k) (i.e. the smallest integer such that u(n,k)=u(n,k+p(n))) p(n)=22,12,22,21,15,9,15,9,15,9....(n=1,2,3,4,5,6...) Hence for n>4 p(n)=15 if n is odd p(n)=9 if n is even.
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FORMULA
| a(1)=5 a(2n)=2n+2 a(2n+1)=3n+2 Ex : for k=1 to 15 u(7, k)=1, 2, 7, 9, 8, 7, 9, 2, 7, 1, 4, 7, 11, 4, 7 hence a(7)=11.
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CROSSREFS
| Sequence in context: A113784 A021651 A200293 * A119807 A184306 A176317
Adjacent sequences: A069211 A069212 A069213 * A069215 A069216 A069217
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2002
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