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A241407 Numbers n such that n^2 == -1 (mod 73).

%I A241407 #19 Sep 21 2024 15:13:45
%S A241407 27,46,100,119,173,192,246,265,319,338,392,411,465,484,538,557,611,
%T A241407 630,684,703,757,776,830,849,903,922,976,995,1049,1068,1122,1141,1195,
%U A241407 1214,1268,1287,1341,1360,1414,1433,1487,1506,1560,1579,1633,1652,1706,1725
%N A241407 Numbers n such that n^2 == -1 (mod 73).
%C A241407 Numbers n such that n == 27 or 46 (mod 73).
%H A241407 Vincenzo Librandi, <a href="/A241407/b241407.txt">Table of n, a(n) for n = 1..1000</a>
%H A241407 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A241407 G.f.: x*(27 + 19*x + 27*x^2)/((1 + x)*(1 - x)^2).
%F A241407 a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.
%F A241407 a(n) = a(n-2) + 73 for all n>2.
%F A241407 a(n) = -27*(-1)^n + 73*floor(n/2).
%t A241407 Select[Range[1500], PowerMod[#, 2, 73] == 72 &] (* or *) CoefficientList[ Series[(27 + 19 x + 27 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]
%t A241407 Table[73n+{27,46},{n,0,30}]//Flatten (* or *) LinearRecurrence[{1,1,-1},{27,46,100},60] (* _Harvey P. Dale_, Jun 13 2017 *)
%o A241407 (Magma) I:=[27,46,100]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];
%o A241407 (Magma) [-27*(-1)^n+73*Floor(n/2): n in [1..50]];
%Y A241407 Cf. similar sequences listed in A155107.
%K A241407 nonn,easy
%O A241407 1,1
%A A241407 _Vincenzo Librandi_, Apr 25 2014