A036128 - OEIS

%I #32 Sep 08 2022 08:44:52

%S 1,2,4,8,16,32,11,22,44,35,17,34,15,30,7,14,28,3,6,12,24,48,43,33,13,

%T 26,52,51,49,45,37,21,42,31,9,18,36,19,38,23,46,39,25,50,47,41,29,5,

%U 10,20,40,27,1,2,4,8,16,32,11,22

%N a(n) = 2^n mod 53.

%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

%H G. C. Greubel, <a href="/A036128/b036128.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

%F a(n) = a(n-1) - a(n-26) + a(n-27). - _R. J. Mathar_, Feb 06 2011

%F a(n) = a(n+52). - _R. J. Mathar_, Jun 04 2016

%p i := pi(53) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

%t PowerMod[2,Range[0,60],53] (* _Harvey P. Dale_, Apr 11 2013 *)

%o (PARI) a(n)=lift(Mod(2,53)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) [Modexp(2, n, 53): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018

%o (Python) for n in range(0, 100): print(int(pow(2, n, 53)), end=' ') # _Stefano Spezia_, Oct 17 2018

%o (GAP) List([0..60],n->PowerMod(2,n,53)); # _Muniru A Asiru_, Oct 17 2018

%Y Cf. A000079 (2^n).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_