A010693 - OEIS

A010693

Periodic sequence: Repeat 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, 2, 3

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OFFSET

0,1

COMMENTS

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

Simple continued fraction of 1+sqrt(5/3) = A176020. - R. J. Mathar, Mar 08 2012

p(n) = a(n-1) is the Abelian complexity function of the Thue-Morse word A010060. - Nathan Fox, Mar 12 2013

LINKS

Table of n, a(n) for n=0..101.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 466

G. Richomme, K. Saari, L. Q. Zamboni, Abelian complexity in minimal subshifts, J. London Math. Soc. 83(1) (2011) 79-95.

G. Richomme, K. Saari, L. Q. Zamboni, Abelian complexity in minimal subshifts, arXiv:0911.2914 [math.CO], 2009.

Index entries for linear recurrences with constant coefficients, signature (0,1).

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

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)

a(n) = A001615(2n)/A001615(n) for n > 0. - Enrique Pérez Herrero, Jun 06 2012

a(n) = floor((n+1)*5/2) - floor((n)*5/2). - Hailey R. Olafson, Jul 23 2014

a(n) = 3 - ((n+1) mod 2). - Wesley Ivan Hurt, Jul 24 2014

MAPLE

A010693:=n->2+(n mod 2): seq(A010693(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2014

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, Apr 21 2008 *)

2 + Mod[Range[0, 100], 2] (* Wesley Ivan Hurt, Jul 24 2014 *)

PadRight[{}, 120, {2, 3}] (* Harvey P. Dale, Jan 20 2023 *)

PROG

(Haskell)

a010693 = (+ 2) . (`mod` 2) -- Reinhard Zumkeller, Nov 27 2012

a010693_list = cycle [2, 3] -- Reinhard Zumkeller, Mar 29 2012

(Magma) [2 + (n mod 2) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2014

(PARI) a(n)=3 - (n+1)%2 \\ Charles R Greathouse IV, May 09 2016

CROSSREFS

Cf. A139421.

Cf. A026549 (partial products).

Sequence in context: A165587 A368405 A356464 * A158478 A139713 A171465