A070402 a(n) = 2^n mod 5.

1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Periodic with period 4: [1, 2, 4, 3]. - Washington Bomfim, Nov 23 2010

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Crossrefs

Cf. A173635.

Programs

GAP

List([0..83],n->PowerMod(2,n,5)); # Muniru A Asiru, Feb 01 2019

Magma

[Modexp(2, n, 5): n in [0..100]]; // Bruno Berselli, Mar 23 2016

Maple

A070402 := proc(n) op((n mod 4)+1,[1,2,4,3]) ; end proc: # R. J. Mathar, Feb 05 2011

Mathematica

PadRight[{}, 100, {1, 2, 4, 3}] (* or *) CoefficientList[Series[(1 + 2 x + 4 x^2 + 3 x^3) / (1 - x^4), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 25 2016 *)
PowerMod[2,Range[0,120],5] (* Harvey P. Dale, Sep 16 2020 *)

PARI

for(n=0, 80, x=n%4; print1(1 + (15*x^2 -5*x -4*x^3)/6, ", ")) \\ Washington Bomfim, Nov 23 2010

Sage

[power_mod(2,n,5) for n in range(0, 105)] # Zerinvary Lajos, Jun 08 2009

Formula

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3).

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

From Washington Bomfim, Nov 23 2010: (Start)

a(n) = 1 + (15*r^2 - 5*r - 4*r^3)/6, where r = n mod 4.

a(n) = A000689(n) - 5*floor(((n-1) mod 4)/2) for n>0. (End)

E.g.f.: (1/2)*(5*exp(x) - 3*cos(x) - sin(x)). - G. C. Greubel, Mar 19 2016