A070471 a(n) = n^3 mod 5.

0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Decimal expansion of 1324/99999. - Vincenzo Librandi, Dec 09 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Crossrefs

Cf. A010874.

Programs

Mathematica

CoefficientList[Series[-x (1 + 3 x + 2 x^2 + 4 x^3)/((x - 1) (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, May 21 2014 *)
PowerMod[Range[0, 100], 3, 5] (* G. C. Greubel, Mar 26 2016 *)
Table[If[Mod[n, 5] == 0, 0, ModularInverse[n, 5]], {n, 0, 100}] (* Jean-François Alcover, May 03 2017 *)

PARI

my(x='x+O('x^99)); concat(0, Vec(-x*(1+3*x+2*x^2+4*x^3)/((x-1)*(1+x+x^2+x^3+x^4)))) \\ Altug Alkan, Mar 27 2016

PARI

a(n) = lift(Mod(n, 5)^3); \\ Michel Marcus, Jun 03 2025

Sage

[power_mod(n,3,5) for n in (0..101)] # Zerinvary Lajos, Oct 29 2009

Formula

a(n) = n^7 mod 5 since 7 == 3 (mod 5-1).

G.f.: -x*(1+3*x+2*x^2+4*x^3) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Dec 10 2010

a(n) = a(n-5). - G. C. Greubel, Mar 26 2016

a(n) = 10 - Sum_{k=1..4} a(n-k) for n > 3. - Nicolas Bělohoubek, Jun 03 2025