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%I #32 Dec 18 2023 14:17:00
%S 1,5,25,14,33,17,11,18,16,6,30,2,10,13,28,29,34,22,36,32,12,23,4,20,
%T 26,19,21,31,7,35,27,24,9,8,3,15,1,5,25,14,33,17,11,18,16,6,30,2,10,
%U 13,28,29,34,22,36,32,12,23,4,20,26,19,21,31,7,35,27,24,9,8,3,15,1,5,25,14
%N a(n) = 5^n mod 37.
%C Period: (1, 5, 25, 14, 33, 17, 11, 18, 16, 6, 30, 2, 10, 13, 28, 29, 34, 22, 36, 32, 12, 23, 4, 20, 26, 19, 21, 31, 7, 35, 27, 24, 9, 8, 3, 15) of length 36. - _Zak Seidov_, Feb 08 2011
%H G. C. Greubel, <a href="/A070384/b070384.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-1) - a(n-18) + a(n-19).
%F G.f.: ( -1-4*x-20*x^2+11*x^3-19*x^4+16*x^5+6*x^6-7*x^7 +2*x^8+10*x^9 -24*x^10+28*x^11-8*x^12-3*x^13-15*x^14-x^15-5*x^16+12*x^17-15*x^18 ) / ( (x-1)*(x^2+1)*(x^4-x^2+1)*(x^12-x^6+1) ). (End)
%F a(n) = 37 - a(n-18). - _Zak Seidov_, Feb 08 2011
%F a(n) = a(n-36). - _G. C. Greubel_, Mar 16 2016
%t a[n_]:=PowerMod[5,n,37];Table[a[n],{n,72}] (* _Zak Seidov_, Feb 08 2011 *)
%o (Sage) [power_mod(5,n,37) for n in range(0,76)] # _Zerinvary Lajos_, Nov 26 2009
%o (PARI) a(n)=lift(Mod(5,37)^n) \\ _M. F. Hasler_, Feb 08 2011
%o (PARI) a(n)=5^(n%36)%37 \\ _M. F. Hasler_, Feb 08 2011
%o (Magma) [Modexp(5, n, 37): n in [0..100]]; // _Vincenzo Librandi_, Jun 29 2016
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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