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%I #21 Feb 27 2017 23:59:53
%S 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,
%T 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,
%U 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
%N a(n) = n^2 mod 21.
%H G. C. Greubel, <a href="/A070443/b070443.txt">Table of n, a(n) for n = 0..1000</a>
%H Sathwik Karnik, <a href="https://arxiv.org/abs/1702.08066">On the classification and algorithmic analysis of Carmichael numbers</a>, arXiv:1702.08066 [math.NT], 2016. See Table 1.
%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F From _R. J. Mathar_, Jul 27 2015: (Start)
%F a(n) = a(n-21).
%F 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)
%t Table[Mod[n^2,21],{n,0,200}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2011 *)
%t PowerMod[Range[0,90],2,21] (* _Harvey P. Dale_, Jan 19 2013 *)
%o (PARI) a(n)=n^2%21 \\ _Charles R Greathouse IV_, Apr 06 2016
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 12 2002
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