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A113471
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Lucas(k)/(3k) for k = 2*3^n, where Lucas(k) is k-th Lucas number (A000032).
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0
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OFFSET
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1,2
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COMMENTS
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a(n) divides a(n+1). a(n+1)/a(n) = {107, 11128427, 12403489755282666163307, 17174107866559209832245996776509546318861182768126017871860347845227, ...}. a(n+1)/a(n) is prime for n = {1, 2, 4}.
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LINKS
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FORMULA
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a(n) = ( Fibonacci[ 2*3^n - 1 ] + Fibonacci[ 2*3^n + 1 ] ) / ( 2*3^(n+1) ). a(n) = A000032[ 2*3^n ] / ( 2*3^(n+1) ).
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MATHEMATICA
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Table[ ( Fibonacci[ 2*3^n - 1 ] + Fibonacci[ 2*3^n + 1 ] ) / ( 2*3^(n+1) ), {n, 1, 5} ]
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CROSSREFS
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Cf. A000032, A016089 = numbers n such that n divides n-th Lucas number. Cf. A128935 = Fibonacci(5^n) / 5^n.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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