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a(n) = n^5 mod 25.
1

%I #17 Dec 07 2019 12:18:23

%S 0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,

%T 24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,

%U 18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1,7,18,24,0,1

%N a(n) = n^5 mod 25.

%C Period 5: repeat [0, 1, 7, 18, 24]. - _Jianing Song_, Apr 06 2019

%H Colin Barker, <a href="/A070609/b070609.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F From _Colin Barker_, Apr 06 2019: (Start)

%F G.f.: x*(1 + 4*x)*(1 + 3*x + 6*x^2) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)).

%F a(n) = a(n-5) for n>4.

%F (End)

%o (Sage) [power_mod(n,5,25)for n in range(0, 87)] # - _Zerinvary Lajos_, Nov 04 2009

%o (PARI) a(n)=n^5%25 \\ _Charles R Greathouse IV_, Apr 06 2016

%o (PARI) concat(0, Vec(x*(1 + 4*x)*(1 + 3*x + 6*x^2) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)) + O(x^80))) \\ _Colin Barker_, Apr 06 2019

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 13 2002