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

0,2

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).

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

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 *)

Prog

(Sage) [power_mod(2, n, 5) for n in range(0, 105)] # Zerinvary Lajos, Jun 08 2009
(PARI) for(n=0, 80, x=n%4; print1(1 + (15*x^2 -5*x -4*x^3)/6, ", ")) \\ Washington Bomfim, Nov 23 2010
(Magma) [Modexp(2, n, 5): n in [0..100]]; // Bruno Berselli, Mar 23 2016
(GAP) List([0..83], n->PowerMod(2, n, 5)); # Muniru A Asiru, Feb 01 2019

Crossrefs

Cf. A173635.

Sequence in context: A229802 A106581 A317612 * A125941 A347270 A275117

Adjacent sequences: A070399 A070400 A070401 * A070403 A070404 A070405

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved