A070443 a(n) = n^2 mod 21.

0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Sathwik Karnik, On the classification and algorithmic analysis of Carmichael numbers, arXiv:1702.08066 [math.NT], 2016. See Table 1.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Programs

Mathematica

Table[Mod[n^2,21],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,90],2,21] (* Harvey P. Dale, Jan 19 2013 *)

PARI

a(n)=n^2%21 \\ Charles R Greathouse IV, Apr 06 2016

Formula

From R. J. Mathar, Jul 27 2015: (Start)

a(n) = a(n-21).

G.f.: -x *(1+x) *(x^18 +3*x^17 +6*x^16 +10*x^15 -6*x^14 +21*x^13 -14*x^12 +15*x^11 +3*x^10 +13*x^9 +3*x^8 +15*x^7 -14*x^6 +21*x^5 -6*x^4 +10*x^3 +6*x^2 +3*x+1) / ( (x-1) *(1+x^6+x^5+x^4+x^3+x^2+x) *(1+x+x^2) *(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12) ). (End)