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A145510
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a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1)=10
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8
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OFFSET
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1,1
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COMMENTS
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General formula for a(n+1)=a(n)^2+2*a(n)-2 and a(1)=k+1 is a(n)=Floor[((k + Sqrt[k^2 + 4])/2)^(2^((n+1) - 1))
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LINKS
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FORMULA
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a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha := 1/2*(11 + sqrt(117)). a(n) = 1 (mod 9).
Recurrence: a(n) = 12*{Product_{k = 1..n-1} a(k)} - 2 with a(1) = 10.
Product {n = 1..inf} (1 + 1/a(n)) = 12/sqrt(117).
Product {n = 1..inf} (1 + 2/(a(n) + 1)) = sqrt(13/9).
(End)
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MATHEMATICA
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aa = {}; k = 10; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
(* or *)
k =9; Table[Floor[((k + Sqrt[k^2 + 4])/2)^(2^(n - 1))], {n, 2, 7}] (*Artur Jasinski*)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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