A070444 a(n) = n^2 mod 22.
0, 1, 4, 9, 16, 3, 14, 5, 20, 15, 12, 11, 12, 15, 20, 5, 14, 3, 16, 9, 4, 1, 0, 1, 4, 9, 16, 3, 14, 5, 20, 15, 12, 11, 12, 15, 20, 5, 14, 3, 16, 9, 4, 1, 0, 1, 4, 9, 16, 3, 14, 5, 20, 15, 12, 11, 12, 15, 20, 5, 14, 3, 16, 9, 4, 1, 0, 1, 4, 9, 16, 3, 14, 5, 20, 15, 12, 11, 12, 15, 20, 5
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..3000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
Programs
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Magma
[n^2 mod (22): n in [0..80]]; // Vincenzo Librandi, May 26 2011
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Mathematica
Table[Mod[n^2,22],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *) PowerMod[Range[0,120],2,22] (* or *) PadRight[{},120,{0,1,4,9,16,3,14,5,20,15,12,11,12,15,20,5,14,3,16,9,4,1}] (* Harvey P. Dale, May 28 2021 *) -
Maxima
makelist(power_mod (n, 2, 22), n, 0, 81); /* Bruno Berselli, May 25 2011 */
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PARI
a(n)=n^2%22 \\ Charles R Greathouse IV, Apr 06 2016
Formula
From R. J. Mathar, Jul 27 2015: (Start)
a(n) = a(n-22).
G.f.: -x*(1 +4*x +9*x^2 +16*x^3 +3*x^4 +14*x^5 +5*x^6 +20*x^7 +15*x^8 +12*x^9 +11*x^10 +12*x^11 +15*x^12 +20*x^13 +5*x^14 +14*x^15 +3*x^16 +16*x^17 +9*x^18 +4*x^19+x^20) / ( (x-1) *(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) *(1+x) *(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) ). (End)