A036131 - OEIS

%I #35 Sep 08 2022 08:44:52

%S 1,2,4,8,16,32,64,61,55,43,19,38,9,18,36,5,10,20,40,13,26,52,37,7,14,

%T 28,56,45,23,46,25,50,33,66,65,63,59,51,35,3,6,12,24,48,29,58,49,31,

%U 62,57,47,27,54,41,15,30,60,53

%N a(n) = 2^n mod 67.

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

%H G. C. Greubel, <a href="/A036131/b036131.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_34">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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

%F a(n) = a(n+66). - _R. J. Mathar_, Jun 04 2016

%F a(n) = a(n-1) - a(n-33) + a(n-34). - _G. C. Greubel_, Oct 17 2018

%e As 2^10 = 1024 = 67 * k + 19 for some k and 0 <= 19 < 67, a(10) = 19. - _David A. Corneth_, Oct 17 2018

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

%t PowerMod[2, Range[0, 100], 67] (* _G. C. Greubel_, Oct 17 2018 *)

%o (PARI) a(n)=lift(Mod(2,67)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) [Modexp(2, n, 67): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018

%o (Python) for n in range(0, 100): print(int(pow(2, n, 67)), end=' ') # _Stefano Spezia_, Oct 17 2018

%o (GAP) List([0..60],n->PowerMod(2,n,67)); # _Muniru A Asiru_, Oct 17 2018

%Y Cf. A000079 (2^n).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_