A109009 a(n) = gcd(n,5).

5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5

Offset: 0

Author

Mitch Harris

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A109004.

Programs

Mathematica

GCD[Range[0,100],5] (* or *) PadRight[{},120,{5,1,1,1,1}] (* Harvey P. Dale, Jun 29 2018 *)

PARI

a(n)=gcd(n,5) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 1 + 4*[5|n], where [x|y] = 1 when x divides y, 0 otherwise.

a(n) = a(n-5).

Multiplicative with a(p^e, 5) = gcd(p^e, 5). - David W. Wilson, Jun 12 2005

From R. J. Mathar, Apr 04 2011: (Start)

Dirichlet g.f.: zeta(s)*(1+4/5^s).

G.f.: ( -5-x-x^2-x^3-x^4 ) / ( (x-1)*(1+x+x^2+x^3+x^4) ). (End)

a(n) = 4*floor(1/2*cos((2*n*Pi)/5)+1/2) + 1.

= 4*floor(((n-1) mod 5)/4) + 1. - Gary Detlefs, Dec 28 2011