|
%I #30 Sep 08 2022 08:44:52
%S 1,5,25,31,14,23,21,11,8,40,12,13,18,43,27,41,17,38,2,10,3,15,28,46,
%T 42,22,16,33,24,26,36,39,7,35,34,29,4,20,6,30,9,45,37,44,32,19,1,5,25,
%U 31,14,23,21,11,8,40,12,13,18,43
%N a(n) = 5^n mod 47.
%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H G. C. Greubel, <a href="/A036127/b036127.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
%F a(n) = (n-46). - _Vincenzo Librandi_, Feb 07 2011
%F a(n) = a(n-1) - a(n-23) + a(n-24). - _R. J. Mathar_, Jun 04 2016
%F a(n) = 47 - a(n+23) for all n in Z. - _Michael Somos_, Oct 17 2018
%p [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t Mod[5^Range[0,100],47] (* _Harvey P. Dale_, Mar 09 2011 *)
%o (PARI) a(n)=lift(Mod(5,47)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(5, n, 47): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%o (GAP) List([0..60],n->PowerMod(5,n,47)); # _Muniru A Asiru_, Oct 18 2018
%Y Cf. A000351 (5^n).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
