A070442 a(n) = n^2 mod 20.

0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Also, n^6 mod 20.

Equivalently n^10 mod 20. - Zerinvary Lajos, Oct 31 2009

Links

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

Crossrefs

Cf. A000290, A008959, A010382, A070431, A070435, A070438, A070452, A159852.

Row 20 of A048152.

Programs

Mathematica

Table[Mod[n^2,20],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 1, 4, 9, 16, 5, 16, 9, 4, 1},95] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,100],2,20] (* or *) PadRight[{},120,{0,1,4,9,16,5,16,9,4,1}] (* Harvey P. Dale, Jan 06 2019 *)

PARI

a(n)=n^2%20 \\ Charles R Greathouse IV, Jun 11 2015

Sage

[power_mod(n,10,20) for n in range(0, 88)] # Zerinvary Lajos, Oct 31 2009

Formula

From Reinhard Zumkeller, Apr 24 2009: (Start)

a(m*n) = a(m)*a(n) mod 20.

a(5*n+k) = a(5*n-k) for k <= 5*n.

a(n+10) = a(n). (End)

G.f. -x*(1+4*x+9*x^2+16*x^3+5*x^4+16*x^5+9*x^6+4*x^7+x^8) / ( (x-1) *(1+x) *(x^4+x^3+x^2+x+1) *(x^4-x^3+x^2-x+1) ). - R. J. Mathar, Aug 27 2013