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.

4, 180, 8, 1820, 12, 320, 9100, 226153980, 267000, 53000, 6377352, 20, 15140424455100, 113296, 519712, 2113761020, 3726964292220, 190060, 183567298683461940, 448036604040, 28, 386460, 70255304, 649641205044600

Offset

1,1

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Example

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

Mathematica

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, Feb 28 2006 *)

Prog

(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; ) ) ) ) }

Crossrefs

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

Sequence in context: A127606 A041945 A300387 * A176351 A330771 A263436

Adjacent sequences: A082390 A082391 A082392 * A082394 A082395 A082396

Keyword

easy,nonn

Author

Cino Hilliard, Apr 14 2003

Extensions

More terms from Robert G. Wilson v, Feb 28 2006

Status

approved