A109008 a(n) = gcd(n,4).
4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).
Crossrefs
Cf. A109004.
Programs
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Haskell
a109008 = gcd 4 a109008_list = cycle [4,1,2,1] -- Reinhard Zumkeller, Nov 25 2013
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Magma
[Gcd(n,4) : n in [0..100]]; // Wesley Ivan Hurt, Aug 31 2014
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Maple
A109008:=n->gcd(n,4): seq(A109008(n), n=0..100); # Wesley Ivan Hurt, Aug 31 2014
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Mathematica
Table[GCD[n, 4], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 31 2014 *) -
PARI
a(n)=gcd(n,4) \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 1 + [2|n] + 2*[4|n] = 2 + (-1)^n + cos(n*Pi/2), where [x|y] = 1 when x divides y, 0 otherwise.
a(n) = a(n-4) for n>3.
Multiplicative with a(p^e) = gcd(p^e, 4). - David W. Wilson, Jun 12 2005
Dirichlet g.f.: (1 + 1/2^s + 2/4^s)*zeta(s). - R. J. Mathar, Feb 28 2011
G.f.: (4+x+2*x^2+x^3)/((1-x)*(1+x)*(1+x^2)). - R. J. Mathar, Apr 04 2011
a(n) = 1 + mod((n-1)^3, 4). - Wesley Ivan Hurt, Aug 31 2014
a(n) = 2 + cos(n*Pi) + cos(n*Pi/2). - Wesley Ivan Hurt, Jul 07 2016
E.g.f.: exp(-x) + 2*exp(x) + cos(x). - Ilya Gutkovskiy, Jul 07 2016
Comments