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

0,3

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).

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)

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 *)

Prog

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

Crossrefs

Sequence in context: A070445 A070444 A120866 * A279403 A330377 A070643

Adjacent sequences: A070440 A070441 A070442 * A070444 A070445 A070446

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved