A070449 a(n) = n^2 mod 27.

0, 1, 4, 9, 16, 25, 9, 22, 10, 0, 19, 13, 9, 7, 7, 9, 13, 19, 0, 10, 22, 9, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 9, 22, 10, 0, 19, 13, 9, 7, 7, 9, 13, 19, 0, 10, 22, 9, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 9, 22, 10, 0, 19, 13, 9, 7, 7, 9, 13, 19, 0, 10, 22, 9, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16

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
• 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, 0, 0, 0, 0, 0, 0, 1).

Programs

Mathematica

Table[Mod[n^2,27],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,100],2,27] (* or *) PadRight[{},100,{0,1,4,9,16,25,9,22,10,0,19,13,9,7,7,9,13,19,0,10,22,9,25,16,9,4,1}] (* Harvey P. Dale, Dec 17 2023 *)

PARI

a(n)=n^2%27 \\ Charles R Greathouse IV, Apr 06 2016

Formula

a(n) = a(n-27). - G. C. Greubel, Mar 24 2016

G.f.:(x + 4*x^2 + 9*x^3 + 16*x^4 + 25*x^5 + 9*x^6 + 22*x^7 + 10*x^8 + 19*x^10 + 13*x^11 + 9*x^12 + 7*x^13 + 7*x^14 + 9*x^15 + 13*x^16 + 19*x^17 + 10*x^19 + 22*x^20 + 9*x^21 + 25*x^22 + 16*x^23 + 9*x^24 + 4*x^25 + x^26)/(1 - x^27). - Vincenzo Librandi, Mar 25 2016