A070431 a(n) = n^2 mod 6.

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

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

a(m*n) = a(m)*a(n) mod 6; a(3*n+k) = a(3*n-k) for k <= 3*n. - Reinhard Zumkeller, Apr 24 2009

Equivalently n^6 mod 6. - Zerinvary Lajos, Nov 06 2009

Equivalently: n^(2*m + 4) mod 6; n^(2*m + 2) mod 6. - G. C. Greubel, Apr 01 2016

Links

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

Crossrefs

Cf. A000290, A008959, A070435, A070438, A070442, A070452, A159852.

Programs

Magma

[n^2 mod 6 : n in [0..100]]; // Wesley Ivan Hurt, Apr 01 2016

Magma

[Modexp(n, 2, 6): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016

Maple

A070431:=n->n^2 mod 6: seq(A070431(n), n=0..100); # Wesley Ivan Hurt, Apr 01 2016

Mathematica

Table[Mod[n^2, 6], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1},{0, 1, 4, 3, 4, 1},101] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,120],2,6] (* or *) PadRight[{},120,{0,1,4,3,4,1}] (* Harvey P. Dale, Aug 11 2019 *)

PARI

a(n)=n^2%6 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[power_mod(n,2,6) for n in range(0, 101)] # Zerinvary Lajos, Oct 30 2009

Formula

G.f.: -x*(1+4*x+3*x^2+4*x^3+x^4)/((x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)). - R. J. Mathar, Jul 23 2009

a(n) = a(n-6). - Reinhard Zumkeller, Apr 24 2009

From G. C. Greubel, Apr 01 2016: (Start)

a(6*m) = 0.

a(2*n) = 4*A011655(n).

a(n) = (1/6)*(13 + 3*(-1)^n - 12*cos(n*Pi/3) - 4*cos(2*n*Pi/3)).

G.f.: (x +4*x^2 +3*x^3 + 4*x^4 +x^5)/(1 - x^6). (End)