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%I #37 Dec 18 2023 14:10:02
%S 1,7,18,2,14,5,4,28,10,8,25,20,16,19,9,1,7,18,2,14,5,4,28,10,8,25,20,
%T 16,19,9,1,7,18,2,14,5,4,28,10,8,25,20,16,19,9,1,7,18,2,14,5,4,28,10,
%U 8,25,20,16,19,9,1,7,18,2,14,5,4,28,10,8,25,20,16,19,9,1,7,18,2,14,5,4
%N a(n) = 7^n mod 31.
%C Sequence is periodic with period length of 15. That a(15) = 1 means that 31 is not prime in Z[sqrt(7)], being factorable as (-1)*(9 - 4*sqrt(7))(9 + 4*sqrt(7)). - _Alonso del Arte_, Oct 11 2012
%H G. C. Greubel, <a href="/A070415/b070415.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n - 15).
%F G.f.: ( -1 -7*x -18*x^2 -2*x^3 -14*x^4 -5*x^5 -4*x^6 -28*x^7 -10*x^8 -8*x^9 -25*x^10 -20*x^11 -16*x^12 -19*x^13 -9*x^14 ) / ( (x-1)*(1 +x^4 + x^3 +x^2 +x)*(1 +x +x^2)*(1 -x +x^3 -x^4 +x^5 -x^7 +x^8) ). (End)
%t PowerMod[7, Range[0, 90], 31] (* _Harvey P. Dale_, Jul 23 2011 *)
%o (Sage) [power_mod(7,n,31) for n in range(0,82)] # _Zerinvary Lajos_, Nov 27 2009
%o (PARI) a(n) = lift(Mod(7, 31)^n); \\ _Altug Alkan_, Mar 20 2016
%o (Magma) [Modexp(7, n, 31): n in [0..100]]; // _Bruno Berselli_, Mar 22 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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