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A010693
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Periodic sequence: Repeat 2,3.
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13
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) = smallest prime divisor of n!! for n >= 2. For biggest prime divisor of n!! see A139421. - Artur Jasinski (grafix(AT)csl.pl), 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). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 466
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FORMULA
| a(n) = 5/2 - ((-1)^n)/2.
a(n) = 2 + n mod 2 = A007395(n) + A000035(n). - Reinhard Zumkeller, Mar 23 2005
a(n) = A020639(A016767(n)) for n>0. - Reinhard Zumkeller, Jan 29 2009
Contribution from Jaume Oliver Lafont, Mar 20 2009: (Start)
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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MATHEMATICA
| 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 (grafix(AT)csl.pl), Apr 21 2008
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CROSSREFS
| Cf. A139421.
Sequence in context: A145384 A117666 A165587 * A158478 A139713 A171465
Adjacent sequences: A010690 A010691 A010692 * A010694 A010695 A010696
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Definition rewritten by Bruno Berselli, Sep 30 2011
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