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A241521 Numbers k such that k^2 == -1 (mod 97).

%I A241521 #23 Mar 12 2025 19:25:45
%S A241521 22,75,119,172,216,269,313,366,410,463,507,560,604,657,701,754,798,
%T A241521 851,895,948,992,1045,1089,1142,1186,1239,1283,1336,1380,1433,1477,
%U A241521 1530,1574,1627,1671,1724,1768,1821,1865,1918,1962,2015,2059,2112,2156,2209,2253
%N A241521 Numbers k such that k^2 == -1 (mod 97).
%C A241521 Numbers k such that k == 22 or 75 (mod 97).
%H A241521 Vincenzo Librandi, <a href="/A241521/b241521.txt">Table of n, a(n) for n = 1..1000</a>
%H A241521 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A241521 G.f.: x*(22 + 53*x + 22*x^2)/((1 + x)*(1 - x)^2).
%F A241521 a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.
%F A241521 a(n) = a(n-2) + 97 for all n>2.
%F A241521 a(n) = -22*(-1)^n + 97*floor(n/2).
%t A241521 Select[Range[1800], PowerMod[#, 2, 97] == 96 &] (* or *) CoefficientList[Series[(22 + 53 x + 22 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]
%o A241521 (Magma) I:=[22,75,119]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];
%o A241521 (Magma) [-22*(-1)^n+97*Floor(n/2): n in [1..50]];
%Y A241521 Cf. similar sequences listed in A155107.
%K A241521 nonn,easy
%O A241521 1,1
%A A241521 _Vincenzo Librandi_, Apr 25 2014