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%I A010693 #58 Mar 26 2024 18:28:07
%S A010693 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,
%T A010693 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,
%U A010693 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
%N A010693 Periodic sequence: Repeat 2,3.
%C A010693 a(n) = smallest prime divisor of n!! for n >= 2. For biggest prime divisor of n!! see A139421. - _Artur Jasinski_, Apr 21 2008
%C A010693 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
%C A010693 Simple continued fraction of 1+sqrt(5/3) = A176020. - _R. J. Mathar_, Mar 08 2012
%C A010693 p(n) = a(n-1) is the Abelian complexity function of the Thue-Morse word A010060. - _Nathan Fox_, Mar 12 2013
%H A010693 INRIA Algorithms Project, <a href="/load/view.php?a=aHR0cDovL2Vjcy5pbnJpYS5mci9zZXJ2aWNlcy9zdHJ1Y3R1cmU/bmJyPTQ2Ng">Encyclopedia of Combinatorial Structures 466</a>
%H A010693 G. Richomme, K. Saari, L. Q. Zamboni, <a href="/load/view.php?a=aHR0cDovL2R4LmRvaS5vcmcvMTAuMTExMi9qbG1zL2pkcTA2Mw">Abelian complexity in minimal subshifts</a>, J. London Math. Soc. 83(1) (2011) 79-95.
%H A010693 G. Richomme, K. Saari, L. Q. Zamboni, <a href="/load/view.php?a=aHR0cDovL2FyeGl2Lm9yZy9hYnMvMDkxMS4yOTE0">Abelian complexity in minimal subshifts</a>, arXiv:0911.2914 [math.CO], 2009.
%H A010693 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlYyNvcmRlcl8wMg">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A010693 a(n) = 5/2 - ((-1)^n)/2.
%F A010693 a(n) = 2 + (n mod 2) = A007395(n) + A000035(n). - _Reinhard Zumkeller_, Mar 23 2005
%F A010693 a(n) = A020639(A016767(n)) for n>0. - _Reinhard Zumkeller_, Jan 29 2009
%F A010693 From _Jaume Oliver Lafont_, Mar 20 2009: (Start)
%F A010693 G.f.:(2+3*x)/(1-x^2).
%F A010693 Linear recurrence: a(0)=2, a(1)=3, a(n)=a(n-2) for n>=2. (End)
%F A010693 a(n) = A001615(2n)/A001615(n) for n > 0. - _Enrique Pérez Herrero_, Jun 06 2012
%F A010693 a(n) = floor((n+1)*5/2) - floor((n)*5/2). - _Hailey R. Olafson_, Jul 23 2014
%F A010693 a(n) = 3 - ((n+1) mod 2). - _Wesley Ivan Hurt_, Jul 24 2014
%p A010693 A010693:=n->2+(n mod 2): seq(A010693(n), n=0..100); # _Wesley Ivan Hurt_, Jul 24 2014
%t A010693 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 *)
%t A010693 2 + Mod[Range[0, 100], 2] (* _Wesley Ivan Hurt_, Jul 24 2014 *)
%t A010693 PadRight[{},120,{2,3}] (* _Harvey P. Dale_, Jan 20 2023 *)
%o A010693 (Haskell)
%o A010693 a010693 = (+ 2) . (`mod` 2)  -- _Reinhard Zumkeller_, Nov 27 2012
%o A010693 a010693_list = cycle [2,3]  -- _Reinhard Zumkeller_, Mar 29 2012
%o A010693 (Magma) [2 + (n mod 2) : n in [0..100]]; // _Wesley Ivan Hurt_, Jul 24 2014
%o A010693 (PARI) a(n)=3 - (n+1)%2 \\ _Charles R Greathouse IV_, May 09 2016
%Y A010693 Cf. A139421.
%Y A010693 Cf. A026549 (partial products).
%K A010693 nonn,easy
%O A010693 0,1
%A A010693 _N. J. A. Sloane_
%E A010693 Definition rewritten by _Bruno Berselli_, Sep 30 2011

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