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A201920 a(n) = 2^n mod 125.

%I A201920 #28 Sep 08 2022 08:46:01
%S A201920 1,2,4,8,16,32,64,3,6,12,24,48,96,67,9,18,36,72,19,38,76,27,54,108,91,
%T A201920 57,114,103,81,37,74,23,46,92,59,118,111,97,69,13,26,52,104,83,41,82,
%U A201920 39,78,31,62,124,123,121,117,109,93,61,122,119,113,101,77,29
%N A201920 a(n) = 2^n mod 125.
%H A201920 G. C. Greubel, <a href="/A201920/b201920.txt">Table of n, a(n) for n = 0..10000</a>
%H A201920 <a href="/index/Rec#order_51">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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).
%F A201920 For n > 50: a(n) = a(n-1) - a(n-50) + a(n-51).
%F A201920 G.f.: (1 + x + 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 - 61x^7 + 3x^8 + 6x^9 + 12x^10 + 24x^11 + 48x^12 - 29x^13 - 58x^14 + 9x^15 + 18x^16 + 36x^17 - 53x^18 + 19x^19 + 38x^20 - 49x^21 + 27x^22 + 54x^23 - 17x^24 - 34x^25 + 57x^26 - 11x^27 - 22x^28 - 44x^29 + 37x^30 - 51x^31 + 23x^32 + 46x^33 - 33x^34 + 59x^35 - 7x^36 - 14x^37 - 28x^38 - 56x^39 + 13x^40 + 26x^41 + 52x^42 - 21x^43 - 42x^44 + 41x^45 - 43x^46 + 39x^47 - 47x^48 + 31x^49 + 63x^50) / ((1-x)*(1+x^2)*(1 - x^2 + x^4 - x^6 + x^8 - x^10 + x^12 - x^14 + x^16 - x^18 + x^20 - x^22 + x^24 - x^26 + x^28 - x^30 + x^32 - x^34 + x^36 - x^38 + x^40 - x^42 + x^44 - x^46 + x^48)).
%F A201920 Periodic with period 100.
%e A201920 a(7) = 2^7 mod 125 = 3.
%t A201920 PowerMod[2,Range[0,100],125] (* _Harvey P. Dale_, Aug 12 2013 *)
%o A201920 (PARI) a(n)=lift(Mod(2,125)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A201920 (Magma) [Modexp(2, n, 125): n in [0..120]]; // _G. C. Greubel_, Oct 17 2018
%o A201920 (GAP) a:=List([0..100],n->PowerMod(2,n,125));; Print(a); # _Muniru A Asiru_, Jan 27 2019
%Y A201920 Cf. A070402, A070336.
%K A201920 nonn,easy
%O A201920 0,2
%A A201920 _Franz Vrabec_, Dec 06 2011