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A010693
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Periodic sequence: Repeat 2,3.
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27
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2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3
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OFFSET
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0,1
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COMMENTS
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a(n) = smallest prime divisor of n!! for n >= 2. For biggest prime divisor of n!! see A139421. - Artur Jasinski, Apr 21 2008
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-3, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=-charpoly(A,-2). - Milan Janjic, Jan 27 2010
p(n) = a(n-1) is the Abelian complexity function of the Thue-Morse word A010060. - Nathan Fox, Mar 12 2013
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LINKS
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FORMULA
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a(n) = 5/2 - ((-1)^n)/2.
G.f.:(2+3*x)/(1-x^2).
Linear recurrence: a(0)=2, a(1)=3, a(n)=a(n-2) for n>=2. (End)
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MAPLE
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MATHEMATICA
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Table[5/2 - (-1)^n/2, {n, 0, 100}] or a = {}; Do[b = First[First[FactorInteger[n!! ]]]; AppendTo[a, b], {n, 2, 1000}]; a (* Artur Jasinski, Apr 21 2008 *)
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PROG
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(Haskell)
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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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EXTENSIONS
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STATUS
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approved
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