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A082394 Let p = n-th prime of the form 4k+3, take the solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and smallest y >= 1; sequence gives value of y.

%I A082394 #19 Feb 28 2018 21:31:16
%S A082394 1,3,3,39,5,273,531,7,69,5967,413,9,9,22419,93,419775,927,6578829,
%T A082394 140634693,5019135,13,313191,650783,1153080099,19162705353,15,15,
%U A082394 400729,231957,8579,7044978537,8219541,5052633,957397,153109862634573,34443,19
%N A082394 Let p = n-th prime of the form 4k+3, take the solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and smallest y >= 1; sequence gives value of y.
%D A082394 C. Stanley Ogilvy, Tomorrow's Math, 1972, p. 119.
%H A082394 Vincenzo Librandi, <a href="/A082394/b082394.txt">Table of n, a(n) for n = 1..1990</a>
%e A082394 For n=3, p = 11, x=10, y=3 since we have 10^2 = 11*3^2 + 1, so a(3) = 3.
%t A082394 PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[ Sqrt[m]]; n = Length[ Last[cf]]; If[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; Transpose[ PellSolve /@ Select[ Prime[ Range[72]], Mod[ #, 4] == 3 &]][[2]] (* _Robert G. Wilson v_, Sep 02 2004 *)
%o A082394 (PARI) p4xp3(n,m) = { forstep(p=3,m,4, for(y=1,n, if(isprime(p), x=y*y*p+1; if(issquare(x), print1(y" "); break; ) ) ) ) }
%Y A082394 Values of x are in A081231. Equals A002349(p). Cf. A082393.
%K A082394 easy,nonn
%O A082394 1,2
%A A082394 _Cino Hilliard_, Apr 14 2003
%E A082394 More terms from _Robert G. Wilson v_, Apr 15 2003; recomputed Sep 03 2004