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 A082393 Let p = n-th prime of the form 4k+1, take the integer solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with the smallest y >= 1; sequence gives value of y. 8

%I

%S 4,180,8,1820,12,320,9100,226153980,267000,53000,6377352,20,

%T 15140424455100,113296,519712,2113761020,3726964292220,190060,

%U 183567298683461940,448036604040,28,386460,70255304,649641205044600

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

%D C. Stanley Ogilvy, Tomorrow's Math, 1972, p. 119.

%H Vincenzo Librandi, <a href="/A082393/b082393.txt">Table of n, a(n) for n = 1..2000</a>

%e For n = 1, p = 5, x=9, y=4 since 9^2 = 5*4^2 + 1, so a(1) = 4.

%t 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]}]; t = {}; Last /@ PellSolve /@ Select[Prime@Range@54, Mod[ #, 4] == 1 &] (* Robert G. Wilson v *)

%o (PARI) p4xp1(n,m) = { forstep(p=1,m,4, for(y=1,n, if(isprime(p), x=y*y*p+1; if(issquare(x), print1(y" "); break; ) ) ) ) }

%Y Values of x are in A081232. Cf. A082394, A081233, A081234. Equals A002349(p).

%K easy,nonn

%O 1,1

%A Cino Hilliard (hillcino368(AT)gmail.com), Apr 14 2003

%E More terms from _Robert G. Wilson v_, Feb 28 2006

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