A070433 a(n) = n^2 mod 9.

0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Also decimal expansion of 4692347/333333333. - Enrique Pérez Herrero, Nov 27 2022

Links

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

Crossrefs

Cf. A000290, A010878, A053879, A070430, A070431.

Programs

Mathematica

Table[Mod[n^2,9],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
PowerMod[Range[0,200],2,9] (* Harvey P. Dale, Jun 11 2011 *)

PARI

a(n)=[0,1,4,0,7,7,0,4,1][n%9+1] \\ Charles R Greathouse IV, Jun 11 2011

PARI

a(n)=n^2%9 \\ Charles R Greathouse IV, Jun 11 2011

Formula

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n-9).

G.f.: ( -x*(1+x)*(x^6+3*x^5-3*x^4+10*x^3-3*x^2+3*x+1) ) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). (End)

a(n) = A010878(A000290(n)) = A010878(n^2). - Enrique Pérez Herrero, Nov 27 2022